International Encyclopedia of Statistical Science

ISBN 9783642048975......Page 1
Absolute Penalty Estimation......Page 2
References and Further Reading......Page 3
Accelerated Lifetime Testing......Page 4
References and Further Reading......Page 5
Factors for Classifications of Sampling Plans......Page 6
A Few Characteristics of a Sampling Plan......Page 7
Actuarial Methods......Page 8
Key Terms......Page 9
Cross References......Page 10
Adaptive Linear Regression......Page 11
What Is Adaptivity?......Page 13
Cross References......Page 14
Adaptive Sampling......Page 15
About the Author......Page 16
Ranking......Page 17
Estimating the CDF or Histogram......Page 18
References and Further Reading......Page 19
African Population Censuses......Page 20
Aggregation Schemes......Page 21
References and Further Reading......Page 23
Agriculture, Statistics in......Page 24
About the Author......Page 25
Cross References......Page 26
Background......Page 27
Derivation......Page 28
Refinements......Page 29
Algebraic Statistics......Page 30
Algebraic Statistics for Contingency Tables......Page 31
References and Further Reading......Page 32
Important Almost Sure Convergence Theorems......Page 33
References and Further Reading......Page 35
Spatial Correlation Measures......Page 36
Spatial Linear Regression......Page 37
Spatial Interaction Data......Page 38
References and Further Reading......Page 39
Purpose of ANCOVA......Page 40
Alternatives to ANCOVA......Page 41
Analysis of Multivariate Agricultural Data......Page 42
References and Further Reading......Page 44
One-Way Analysis of Variance......Page 45
The normalnormalF-Test......Page 46
Introduction......Page 47
Departures from Equal Variances......Page 48
Tests for Normality......Page 49
Transformations to Correct Lack of Homoscedasticity......Page 50
References and Further Reading......Page 51
Outline of Derivation......Page 53
Anderson–Darling Tests with Unknown Parameters......Page 54
Introduction......Page 55
Approximations to the Densities of Sufficient Estimators......Page 56
Introduction......Page 58
Curve Fitting......Page 59
Asymptotic Expansions......Page 60
Attitudes and Perspectives......Page 61
Symmetric Measures......Page 62
Asymmetric Measures......Page 63
Concluding Comment......Page 64
History......Page 65
Censoring and Truncation......Page 66
References and Further Reading......Page 67
Asymptotic Normality......Page 68
Definition in the General Case......Page 69
A Compromise: The Hodges–Lehmann Location Estimator......Page 70
Fixed Width Confidence Intervals and ARE......Page 71
Cross References......Page 72
Asymptotic Relative Efficiency of Two Tests......Page 73
Bahadur Efficiency......Page 74
References and Further Reading......Page 75
References and Further Reading......Page 76
Autocorrelation in Regression......Page 77
Ingredients of Probability Spaces......Page 78
Axioms of Probability......Page 79
References and Further Reading......Page 80
Cross References......Page 82
Statistics in Banking: The Colombian Perspective......Page 83
References and Further Reading......Page 84
Bartlett Correction......Page 85
Bartlett-Type Correction......Page 86
References and Further Reading......Page 87
Bartlett\'s Test......Page 88
References and Further Reading......Page 89
About the Author......Page 90
The Economist 2000......Page 91
Laplace and Venn......Page 92
Priors and Priors......Page 93
Lindley and Territory......Page 94
Curvature: The Bane of Bayes......Page 95
Why Bayes?......Page 96
References and Further Reading......Page 97
Bayesian Approach of the Unit Root Test......Page 98
Conclusions......Page 99
Bayesian Nonparametric Statistics......Page 100
References and Further Reading......Page 101
Bayesian P-Values......Page 102
About the Authors......Page 104
Bayesian Reliability Modeling......Page 105
References and Further Reading......Page 106
Observation Models......Page 107
Introduction......Page 108
Probability as a Measure of Conditional Uncertainty......Page 110
Statistical Inference and Decision Theory......Page 111
Exchangeability and Representation Theorem......Page 112
The Bayesian Paradigm......Page 113
The Learning Process......Page 114
Predictive Distributions......Page 117
Asymptotic Behavior......Page 118
Inference Summaries......Page 119
Estimation......Page 120
Hypothesis Testing......Page 122
Reference Analysis......Page 124
Reference Distributions......Page 125
Frequentist Properties......Page 129
Objectivity......Page 131
Applicability......Page 132
References and Further Reading......Page 133
Bayesian Statistics......Page 134
Why to Become Frequentist/Bayesian?......Page 135
References and Further Reading......Page 136
Bayesian vs. Classical Point Estimation: A Comparative Overview......Page 137
Introduction......Page 139
Other Solutions......Page 140
References and Further Reading......Page 141
The Best Linear Unbiased Estimator (BLUE) of Xbold0mu mumu No Author Given......Page 142
Two Linear Models......Page 143
About the Authors......Page 144
Beta Distribution......Page 145
Bias Analysis......Page 146
Confounding......Page 147
References and Further Reading......Page 148
Introduction......Page 149
General Formula......Page 150
Binomial Distribution......Page 153
Bioinformatics......Page 155
References and Further Reading......Page 156
Biopharmaceutical Research, Statistics in......Page 157
About the Author......Page 158
Biostatistics......Page 159
Continuous Bivariate Distributions......Page 161
Discrete Bivariate Distributions......Page 164
Dependence......Page 165
Bootstrap Asymptotics......Page 167
References and Further Reading......Page 169
The Basic Idea......Page 170
Extension to Dependent Data......Page 171
When and Why Bootstrap Can Fail to Work......Page 172
About the Authors......Page 173
References and Further Reading......Page 174
The Borel–Cantelli Lemma......Page 175
Generalizations......Page 176
Box–Cox Transformation......Page 177
Autocorrelation and Partial Autocorrelation Functions......Page 179
About the Author......Page 181
Brownian Motion and the Wiener Process......Page 182
Semigroups Associated with Markov Transition Probability Functions......Page 184
Forecasting, Planning, and Goals......Page 186
Time Series Methods......Page 187
References and Further Reading......Page 188
Business Intelligence......Page 189
An Overview and Definitions......Page 190
The Future of Business Statistics Education......Page 191
Business Surveys......Page 192
References and Further Reading......Page 195
Calibration......Page 196
Introduction......Page 197
 Measures of Association......Page 198
Cross References......Page 199
Procedure......Page 200
Interpretation......Page 201
Careers in Statistics......Page 202
Medicine......Page 203
Cross References......Page 204
Types of Case-Control Studies......Page 205
References and Further Reading......Page 206
Contingency Tables......Page 207
References and Further Reading......Page 208
Basics of Graph Theory......Page 209
Interpretations of Graphs......Page 210
Control: Manipulation Versus Conditioning......Page 211
Separation......Page 212
Bias and Confounding......Page 213
Estimation of Causal Effects......Page 214
Questions of Discovery......Page 215
References and Further Reading......Page 216
Counterfactuals and Potential Outcomes......Page 217
From Randomized to Observational Inference......Page 218
Canonical Inference......Page 219
Cross References......Page 220
References and Further Reading......Page 221
Basic Concepts on Censored Data......Page 222
Type-II Censoring......Page 223
Cross References......Page 224
History......Page 225
Planning the Census......Page 226
Collecting the Information......Page 227
Problems in Census Taking and Issues for the Future......Page 228
Introduction......Page 229
Different Versions of the Central Limit Theorem......Page 230
Rates of Convergence to Normality......Page 232
Asymptotic Distributions of Statistics not Expressible as Sums of Random Variables......Page 233
Central Limit Theorems for Stochastic Processes......Page 234
Chaotic Modelling......Page 235
References and Further Reading......Page 238
Characteristic Functions......Page 239
Chebyshev\'s Inequality......Page 240
Chemometrics......Page 241
References and Further Reading......Page 242
Cross References......Page 243
Chernoff Faces......Page 244
About the Author......Page 245
Chi-Square Distribution......Page 246
Chi-Square Goodness-of-Fit Tests: Drawbacks and Improvements......Page 247
References and Further Reading......Page 250
Likelihood Ratio Chi-Square......Page 251
Summary......Page 252
Chi-Square Tests......Page 253
References and Further Reading......Page 254
Clinical Trials, History of......Page 255
References and Further Reading......Page 256
Clinical Trials: An Overview......Page 257
Side Effect of Drugs......Page 260
Large Clinical Trials: Meta-analysis......Page 261
About the Author......Page 262
Cluster Analysis: An Introduction......Page 263
Cluster Sampling......Page 266
Collapsibility in Contingency Tables......Page 268
Collapsibility in Regression Models......Page 269
References and Further Reading......Page 270
Comparability: Definition and Assessment......Page 271
Comparability in Official Statistics......Page 272
References and Further Reading......Page 273
Complier-Average Causal Effect (CACE) Estimation......Page 274
About the Author......Page 275
Composite Indicators......Page 276
What Is Computational Statistics?......Page 277
Symbolic/Exact Methods......Page 278
Future Directions......Page 279
Conditional Expectation and Probability......Page 280
Confidence Distributions......Page 283
Confidence Interval......Page 284
Introduction......Page 285
The Potential-Outcome Model of Confounding......Page 286
Confounders (Confounding Factors) and Covariate Imbalance......Page 287
Adjustment for Confounding......Page 288
Confounder Selection......Page 289
References and Further Reading......Page 290
Contagious Distributions......Page 291
References and Further Reading......Page 292
Continuity Correction......Page 293
Introduction......Page 294
Some Modifications of the Basic Chart......Page 295
Some Other Types of Control Charts......Page 296
EWMA Charts......Page 297
Introduction......Page 298
Convergence in Probability......Page 299
Almost Sure Convergence......Page 300
References and Further Reading......Page 301
Cook\'s Distance......Page 302
Copulas......Page 303
References and Further Reading......Page 305
Pricing Applications......Page 306
Risk Management......Page 307
Copulas and Temporal Dependence in Finance......Page 308
Financial Prices Dynamics and Copulas......Page 309
Dependence......Page 310
Copulas......Page 311
Acknowledgments......Page 312
Introduction......Page 313
Expansion Formulas......Page 314
Error Bounds......Page 315
Population Correlation Coefficient......Page 316
A Sample Correlation Coefficient......Page 317
Partial Correlations......Page 318
Correspondence Analysis......Page 319
References and Further Reading......Page 321
References and Further Reading......Page 322
Cramér–Rao and UMVUE......Page 323
Introduction......Page 324
All Parameters Known......Page 325
About the Author......Page 326
The Basic Multilevel Model......Page 327
About the Author......Page 328
Cross-Covariance Operators......Page 329
References and Further Reading......Page 330
The Development of Data Analysis......Page 332
The Techniques of Data Analysis......Page 333
Three-Way Data Analysis......Page 334
Data Depth......Page 335
Data Mining......Page 337
References and Further Reading......Page 339
Data Mining Time Series Data......Page 340
Time Series Representations......Page 341
References and Further Reading......Page 342
Introduction......Page 343
Computer Science Approaches......Page 344
References and Further Reading......Page 345
Introduction and Summary......Page 346
Decision Theory: An Introduction......Page 347
Decision Theory: An Overview......Page 350
Decision Matrices......Page 351
Probability or Uncertainty......Page 352
The Maximax Rule......Page 353
Expected Utility......Page 354
Ellsberg\'s Paradox......Page 355
References and Further Reading......Page 356
Example......Page 357
Dynamic Regression Models......Page 360
Modeling of Degradation Process......Page 361
Degrees of Freedom......Page 364
DF in Terms of Dimensions and Parameters......Page 365
Degrees of Freedom in Statistical Inference......Page 366
About the Author......Page 367
Macro-Level Focus......Page 368
Micro-Level Processes......Page 369
References and Further Reading......Page 370
Demographic Data......Page 371
Data Cleaning and Careful Description......Page 372
References and Further Reading......Page 373
Density Ratio Model......Page 374
Design for Six Sigma......Page 375
Design of Experiments: A Pattern of Progress......Page 377
Introduction......Page 378
Choice of Design for GLMs......Page 379
References and Further Reading......Page 380
Detecting Outliers of a Simulated normalnormalAR(1) Time Series......Page 381
Simulation of Simultaneous Transfer Function (STF) Model......Page 382
Turns in Business Cycles......Page 383
Models......Page 384
References and Further Reading......Page 385
Dickey-Fuller Tests......Page 386
Discriminant Analysis: An Overview......Page 389
PDA Versus DDA......Page 391
More Issues and Problems......Page 392
Introduction......Page 393
Exponential Dispersion Models......Page 394
Tweedie Exponential Dispersion Models......Page 396
References and Further Reading......Page 397
Distance Measures......Page 398
Distance Sampling......Page 399
About the Authors......Page 400
Geometric Distribution of Order normalnormalk......Page 401
Binomial Distribution of Order normalnormalk......Page 402
Introduction......Page 403
Cardinal Measures......Page 404
Statistical Inferences......Page 405
Divisible Statistics......Page 406
Dummy Variables......Page 408
Durbin–Watson Test......Page 409
References and Further Reading......Page 410
Econometrics......Page 412
References and Further Reading......Page 413
About the Author......Page 415
Misuse of Certain Statistics......Page 416
About the Author......Page 417
Sample Surveys......Page 418
System of National Accounts......Page 419
An Example......Page 420
About the Author......Page 421
Formal Expansion......Page 422
Cornish–Fisher EE......Page 423
Effect Modification and Biological Interaction......Page 424
Biological Interaction......Page 425
References and Further Reading......Page 426
Effect Size......Page 427
References and Further Reading......Page 429
Eigenvalue, Eigenvector and Eigenspace......Page 430
References and Further Reading......Page 431
Empirical Likelihood: IID Case......Page 432
Pseudo-EL: Complex Surveys......Page 433
Empirical Processes......Page 434
References and Further Reading......Page 436
Properties of H......Page 437
Cross-Entropy (Divergence)......Page 438
Parameterized Generalizations......Page 439
References and Further Reading......Page 440
Entropy Functional......Page 441
ANODIV......Page 442
Characterization......Page 443
Some Applications of CE......Page 444
About the Author......Page 445
References and Further Reading......Page 446
Environmental Monitoring, Statistics Role in......Page 447
Equivalence Testing......Page 448
Birkhoff\'s Ergodic Theorem......Page 450
Kingman\'s Subadditive Ergodic Theorem......Page 451
Erlang\'s Formulas......Page 452
First Erlang Formula......Page 453
Exact Decomposition Formulas for the Multi-Server Erlang Loss-Delay Queue......Page 454
References and Further Reading......Page 455
Introduction......Page 456
Defining Point Estimators......Page 457
Evaluating Point Estimators......Page 458
References and Further Reading......Page 459
Estimation Problems for Random Fields......Page 460
How to Construct Estimators?......Page 461
The Plug in Principle......Page 462
M-Estimators......Page 463
About the Author......Page 464
Responsibilities......Page 465
About the Author......Page 466
Different Observation Plans......Page 467
Censoring......Page 468
Parallel and Interdependent Processes......Page 469
References and Further Reading......Page 470
Introduction and Simple Case......Page 471
Composite Case: Non-Group Model......Page 472
Exact Inference for Categorical Data......Page 473
Ibold0mu mumu No Author GivenJ Tables......Page 474
Exchangeability......Page 475
About the Authors......Page 476
Computing Rules......Page 477
References and Further Reading......Page 478
Components of Experimental Design......Page 479
Cross References......Page 480
Expert Systems......Page 481
Introduction......Page 483
 Same Data, Different Methods, Different Outcomes......Page 484
Conclusion......Page 486
Exploratory Data Analysis......Page 487
About the Author......Page 488
Exponential and Holt-Winters \rSmoothing......Page 489
Exponential Family Models......Page 491
References and Further Reading......Page 493
Introduction......Page 494
Extreme Value Theory and Max-Stability......Page 495
Extremes of Gaussian Processes......Page 497
References and Further Reading......Page 499
Definition of the F Distribution......Page 500
On Numerical Computations......Page 501
Background......Page 502
The Literature......Page 503
Factorial Experiments......Page 504
Multiple Hypothesis Testing......Page 505
Mathematical Definitions......Page 506
Control and Estimation......Page 507
About the Author......Page 508
Introduction......Page 509
Mother–Baby Structures......Page 510
Analytical Options......Page 511
Stability Analysis......Page 512
References and Further Reading......Page 514
Ongoing and Upcoming Issues......Page 515
Introduction......Page 516
Generalized Fiducial Distribution......Page 517
Examples......Page 518
References and Further Reading......Page 519
Financial Return Distributions......Page 520
References and Further Reading......Page 521
First Exit Time Problem......Page 522
References and Further Reading......Page 523
Analytical Time Scale......Page 524
Fisher Exact Test......Page 525
Fisher-Tippett Theorem......Page 526
Five-Number Summaries......Page 527
Forecasting Methods......Page 528
Forecasting Canon......Page 532
Be Conservative When Uncertain......Page 534
Forecasting with ARIMA Processes......Page 535
Computation of Forecasts......Page 536
What Can Be Forecast?......Page 537
The Basic Steps in a Forecasting Task......Page 538
Percentage Errors......Page 539
Introduction......Page 540
Paternity Determination......Page 541
References and Further Reading......Page 542
Kolmorgorov\'s Axioms......Page 543
References and Further Reading......Page 544
Frailty Model......Page 545
References and Further Reading......Page 546
Fraud in Statistics......Page 547
Frequentist Hypothesis Testing: A Defense......Page 548
Cross References......Page 551
Introduction......Page 552
FBST Definition......Page 553
Cross References......Page 554
Functional Data Analysis......Page 555
Introduction......Page 556
Functional Derivatives......Page 557
Statistical Functionals and the Bootstrap......Page 558
Probability and Statistics with Fuzziness......Page 559
Fuzzy Clustering and Classification......Page 560
Fuzzy Principal Component Analysis......Page 561
Statistical Hypothesis Tests and Confidence Intervals......Page 562
References and Further Reading......Page 563
Fuzzy Set Theory and Probability Theory: What is the Relationship?......Page 564
References and Further Reading......Page 566
Definitions......Page 567
The Algebra of Fuzzy Subsets......Page 568
Explanation......Page 569
Preliminary......Page 570
References and Further Reading......Page 571
Properties of Estimators......Page 574
Cross References......Page 575
Gaussian Processes......Page 576
About the Author......Page 577
Gauss-Markov Theorem......Page 578
Historical Notes......Page 579
References and Further Reading......Page 581
General Linear Models......Page 583
References and Further Reading......Page 585
Generalized Extreme Value Family of Probability Distributions......Page 586
Cumulative Distribution Function......Page 587
References and Further Reading......Page 588
Generalized Hyperbolic Distributions......Page 590
References and Further Reading......Page 591
Theory......Page 592
Goodness-of-Fit......Page 595
Application......Page 596
References and Further Reading......Page 597
Illustration for the Binary Case......Page 598
GQL Estimation: A Generalization of the QL Estimation to the Correlated Data......Page 599
Generalized Rayleigh Distribution......Page 600
References and Further Reading......Page 603
Generalizations......Page 604
About the Author......Page 605
Introduction......Page 606
Properties......Page 607
About the Author......Page 608
Geometric Mean......Page 609
Kriging Predictions......Page 610
Block Kriging......Page 611
About the Author......Page 612
Generalizations of Glivenko-Cantelli Theorem......Page 613
A Simple Comparative Experiment......Page 615
A Split Plot Experiment......Page 616
About the Author......Page 618
Graphical Markov Models......Page 619
References and Further Reading......Page 621
Nonresponse in Ranked Set Sampling......Page 622
Harmonic Mean......Page 623
Cross References......Page 624
Cross References......Page 625
Cox Regression Model......Page 626
Definition of HTD......Page 627
Remarks......Page 628
Heteroscedastic Time Series......Page 629
Introduction......Page 631
Detection of Heteroscedasticity......Page 632
Remedial Measures......Page 633
References and Further Reading......Page 634
About the Author......Page 635
Hodges-Lehmann Estimators......Page 636
References and Further Reading......Page 637
Properties of the H–T Estimator......Page 638
References and Further Reading......Page 639
Hyperbolic Secant Distributions and Generalizations......Page 641
Hypergeometric Distribution and Its Application in Statistics......Page 642
References and Further Reading......Page 644
Overview......Page 646
Applications in Statistics and Decision Theory......Page 647
About the Authors......Page 648
References and Further Reading......Page 649
Applications......Page 650
Imputation......Page 651
References and Further Reading......Page 653
IBDs with High Efficiency Factors......Page 654
Some Applications of IBDs......Page 655
Incomplete Data in Clinical and Epidemiological Studies......Page 656
Definition......Page 657
The Jevons Index......Page 658
The Fisher Index......Page 659
Areas of Research......Page 660
Control Charts......Page 661
Six Sigma......Page 662
Inference Under Informative Probability Sampling......Page 663
References and Further Reading......Page 665
References and Further Reading......Page 666
About the Author......Page 667
Instrumental Variables......Page 668
Insurance, Statistics in......Page 670
Integrated Statistical Databases......Page 672
Interaction......Page 674
Interactive and Dynamic Statistical Graphics......Page 675
Main Concepts of Interactive and Dynamic Statistical Graphics......Page 676
Software for Interactive and Dynamic Statistical Graphics......Page 677
An Interactive Graphical Example......Page 678
Further Reading and Viewing......Page 679
Internet Survey Methodology: Recent Trends and Developments......Page 680
References and Further Reading......Page 682
Intervention Model......Page 683
References and Further Reading......Page 685
Intraclass Correlation Coefficient......Page 686
Characteristics of IG Distribution......Page 688
Inverse Sampling......Page 689
Inversion of Bayes\' Formula for Events......Page 691
Cross References......Page 695
Itô Integral......Page 696
References and Further Reading......Page 697
Variance Estimation......Page 698
References and Further Reading......Page 699
James–Stein Estimator in the Original Problem......Page 700
References and Further Reading......Page 701
Testing Normality of Unobserved Regression Residuals......Page 702
Jump Regression Analysis......Page 703
2-D Jump Regression Analysis......Page 704
References and Further Reading......Page 705
Kalman Filtering......Page 706
Implementation Methods......Page 707
References and Further Reading......Page 709
Kaplan-Meier Estimator......Page 710
Introduction......Page 711
Specific Category Kappa......Page 712
Statistical Inferences......Page 713
Kendall\'s Tau......Page 714
Kendall\'s Tau-b......Page 715
Background......Page 716
Khmaladze Transformation......Page 717
Cross References......Page 718
Kolmogorov-Smirnov Test......Page 719
Kullback-Leibler Divergence......Page 721
References and Further Reading......Page 722
Kurtosis: An Overview......Page 723
References and Further Reading......Page 724
Large Deviations and Applications......Page 726
Laws of Large Numbers......Page 727
Cross References......Page 729
My SQU Experience......Page 730
Least Absolute Residuals Procedure......Page 731
References and Further Reading......Page 732
Least Squares......Page 733
Introduction......Page 734
The Variance Gamma Process......Page 735
Life Expectancy......Page 736
References and Further Reading......Page 737
Life Table......Page 738
Introduction......Page 739
Inference......Page 740
Extensions to Likelihood......Page 741
References and Further Reading......Page 742
Limit Theorems of Probability Theory......Page 743
Linear Mixed Models......Page 745
About the Author......Page 746
Aspects of Data, Model and Notation......Page 747
Background......Page 748
Algebraic Properties of Least Squares......Page 749
Comparing Two Basic Linear Regression Models......Page 750
References and Further Reading......Page 751
Local Asymptotic Mixed Normal Family......Page 752
Location-Scale Distributions......Page 753
About the Author......Page 754
References and Further Reading......Page 755
Logistic Regression......Page 756
Logistic Distribution......Page 759
Definition and Properties......Page 761
About the Author......Page 762
Loss Function......Page 763
References and Further Reading......Page 764
Definition......Page 766
Intrinsic Priors for Model Selection and Hypothesis Testing......Page 767
Marine Research, Statistics in......Page 768
Cross References......Page 769
Introduction......Page 770
Metropolis–Hastings method......Page 771
About the Author......Page 772
Introduction......Page 773
Discrete Time Markov Chains......Page 774
Markov Chains and Markov Processes......Page 775
Markov Processes......Page 776
Cross References......Page 777
Martingale Central Limit Theorem......Page 778
References and Further Reading......Page 779
Martingales......Page 780
References and Further Reading......Page 781
Introduction......Page 782
Atmospheric Temperature, Ta......Page 783
Parametric Analysis......Page 784
A Differential Equation of CO2 in the Atmosphere......Page 785
References and Further Reading......Page 786
Maximum Entropy Method for Estimation of Missing Data......Page 787
Mean, Median and Mode......Page 788
Introduction......Page 789
The Median......Page 790
The Mode......Page 791
Mean Residual Life......Page 792
References and Further Reading......Page 793
Foundations of Probability: Fields and Sigma-Fields......Page 794
Integration......Page 795
Parts of MEM......Page 796
Functional Method: Corrected Score......Page 797
Nonparametric Estimation......Page 798
Measurement of Economic Progress......Page 799
References and Further Reading......Page 800
Measurement of Uncertainty......Page 801
References and Further Reading......Page 803
Measures of Agreement......Page 804
Measures of Dependence......Page 805
References and Further Reading......Page 806
References and Further Reading......Page 807
Clinical Trials......Page 808
References and Further Reading......Page 809
Illustrative Methodological Developments......Page 810
Conclusion......Page 811
Introduction......Page 812
Qualitative Grounds......Page 813
Inference for the REM......Page 814
References and Further Reading......Page 815
Method Comparison Studies......Page 816
Methods of Moments Estimation......Page 817
Minimum Variance Unbiased......Page 818
So What Is Statistics?......Page 820
References and Further Reading......Page 821
Misuse of Statistics......Page 822
References and Further Reading......Page 824
Early Developments......Page 825
Relationship to Other Methods of Multivariate Analysis......Page 826
References and Further Reading......Page 827
Statistical Problems......Page 828
EM Algorithm......Page 829
References and Further Reading......Page 830
Bayesian Approach......Page 831
Model Selection in High Dimensional Models......Page 832
References and Further Reading......Page 833
Stochastic Models for Spatial Data......Page 834
Bayesian Kriging......Page 835
Generalized Linear Geostatistical Models......Page 836
Modeling Count Data......Page 837
Modeling Randomness Using System Dynamics Concepts......Page 840
Modeling Survival Data......Page 842
About the Author......Page 844
First construction......Page 845
Fourth Construction......Page 846
About the Author......Page 847
Moderate Deviations......Page 848
Moderating and Mediating Variables in Psychological Research......Page 850
Moment Generating Function......Page 853
The Basic Monte Carlo Principle and Its Extensions......Page 855
MCMC Methods......Page 856
Some Uses of Monte Carlo in Statistics......Page 857
About the Author......Page 858
Introduction......Page 859
Starting Point......Page 860
Three Monty Hall Problems......Page 861
Answer to Marilyn Vos Savant\'s Q-0: Should You Switch Doors?......Page 862
Discussion......Page 863
About the Authors......Page 864
Neyman-Pearson Theory......Page 865
Invariant and Unbiased Tests......Page 866
Smoothing Using Two-Sided Moving Averages......Page 867
Centered Moving Averages......Page 868
Moving Average Processes......Page 869
Multicollinearity......Page 870
Usual Clustering Problems......Page 871
Modified Agglomerative Hierarchical Approach......Page 872
Basic Definitions......Page 873
Preference Modeling......Page 874
References and Further Reading......Page 875
Multidimensional Scaling......Page 876
Multidimensional Scaling: An Introduction......Page 879
Multilevel Analysis, Hierarchical Linear Models......Page 880
More Than Two Levels......Page 881
Inference......Page 882
Multinomial Distribution......Page 883
The Multi-Party Inference Reality......Page 885
Uncongeniality in Multiple Imputation Inference......Page 887
References and Further Reading......Page 888
Any Contrast Comparisons......Page 889
About the Authors......Page 890
A General Multiple Comparisons Problem......Page 891
Example......Page 892
Multiple Imputation and Combining Estimates......Page 893
Bootstrap EM......Page 894
Software......Page 895
Multiple Statistical Decision Theory......Page 896
Probability and Single Stage Sampling......Page 897
Cluster and Multistage Sampling......Page 898
References and Further Reading......Page 899
Function Selection Procedure (FSP)......Page 900
Multivariable Fractional Polynomial (MFP) Procedure......Page 901
About the Authors......Page 902
Multivariate Analysis of Variance (MANOVA)......Page 903
Multivariate Data Analysis: An Overview......Page 905
About the Author......Page 906
Multivariate Normal Distributions......Page 908
References and Further Reading......Page 910
Multivariate Outliers......Page 911
References and Further Reading......Page 912
Multivariate Rank Procedures : Perspectives and Prospectives......Page 913
Multivariate Reduced-Rank Regression......Page 914
Multivariate Statistical Analysis......Page 916
Cross References......Page 919
References and Further Reading......Page 920
Some Properties......Page 921
Student t Distributions......Page 923
Gamma Distributions......Page 924
Distributions of Latent Roots......Page 925
Binomial, Multinomial, and Related......Page 926
Other Distributions......Page 927
References and Further Reading......Page 928
Multivariate Statistical Process Control......Page 929
Multivariate Statistical Simulation......Page 931
Multivariate Techniques: Robustness......Page 933
References and Further Reading......Page 935
National Account Statistics......Page 938
Network Models in Probability and Statistics......Page 940
References and Further Reading......Page 941
Network Sampling......Page 942
Types of Neural Network......Page 943
Supervised Neural Networks......Page 944
Unsupervised Neural Networks......Page 945
Neyman-Pearson Lemma......Page 946
References and Further Reading......Page 947
Nonlinear Mixed Effects Models......Page 948
About the Author......Page 950
Introduction\r......Page 951
On the Existence of the Least Square Estimators......Page 952
Optimality Criteria......Page 953
Nonlinear Regression......Page 954
Nonlinear Time Series Analysis......Page 956
About the Author......Page 958
Nonparametric Density Estimation......Page 959
Meanings of the Word ``Nonparametric\'\'......Page 960
Wavelet Estimation......Page 961
References and Further Reading......Page 962
Nonparametric Estimation Based on Incomplete Observations......Page 963
Nonparametric Models for ANOVA and ANCOVA Designs......Page 965
References and Further Reading......Page 968
Overview......Page 969
About the Author......Page 970
Nonparametric Rank Tests......Page 971
Nonparametric Regression Based on Ranks......Page 973
The Statistical Model......Page 975
Nonparametric Statistical Inference......Page 978
About the Authors......Page 979
Non-probability Sampling Survey Methods......Page 980
Sampling from Mobile Human Populations within Small Areas......Page 981
References and Further Reading......Page 982
Nonresponse in Surveys......Page 983
References and Further Reading......Page 984
Nonresponse in Web Surveys......Page 985
References and Further Reading......Page 988
Coverage Errors......Page 989
Instrument Errors......Page 990
References and Further Reading......Page 991
Inversion......Page 992
Brief Historical Background......Page 996
Important Properties and Results......Page 997
Importance of Normal Distribution in Statistics......Page 998
References and Further Reading......Page 999
Normal Scores......Page 1000
The Importance of Testing for Normality......Page 1001
Types of Normality Tests......Page 1002
About the Author......Page 1003
References and Further Reading......Page 1004
Null-Hypothesis Significance Testing: Misconceptons......Page 1007
References and Further Reading......Page 1009
Newton–Cotes Quadrature......Page 1010
Determination of Weights in Gaussian Quadrature......Page 1011
Error in Monte Carlo Quadrature......Page 1012
Numerical Methods for Stochastic Differential Equations......Page 1013
References and Further Reading......Page 1014
Omnibus Test for Departures from Normality......Page 1016
About the Authors......Page 1017
Textbooks......Page 1019
Data Analysis......Page 1020
Introduction......Page 1021
Optimality Criteria......Page 1022
About the Author......Page 1023
Exact and Approximate Designs......Page 1024
Optimality Conditions and Algorithms......Page 1025
Optimal Shrinkage Estimation......Page 1026
Optimal Shrinkage Estimation Strategy......Page 1027
About the Author......Page 1028
Optimal Shrinkage Preliminary Test Estimation......Page 1029
Shrinkage Preliminary Test Estimation......Page 1030
Optimal Statistical Inference in Financial Engineering......Page 1031
Cross References......Page 1032
Optimal Stopping Rules......Page 1033
About the Author......Page 1034
Distortions of Hypothetical Models......Page 1035
Cross References......Page 1037
Criteria of Optimality......Page 1038
About the Author......Page 1039
Order Statistics......Page 1040
Ordered Statistical Data: Recent Developments......Page 1041
References and Further Reading......Page 1043
Outliers......Page 1044
Accommodation......Page 1045
References and Further Reading......Page 1046
Panel Data......Page 1048
Introduction......Page 1049
Nonparametric Approach to Reliability......Page 1050
Parametric Versus Nonparametric Tests......Page 1052
Introduction......Page 1053
Restricted Pareto Sampling......Page 1054
Introduction......Page 1055
Partial Least Squares Regression......Page 1056
Introduction......Page 1057
Design of a Pattern Classifier......Page 1058
Preliminaries......Page 1059
Discrete Distributions......Page 1060
Permutation Tests......Page 1061
Pharmaceutical Statistics: Bioequivalence......Page 1063
Philosophical Foundations of Statistics......Page 1064
References and Further Reading......Page 1065
Philosophy of Probability......Page 1066
References and Further Reading......Page 1069
Point Processes......Page 1070
About the Author......Page 1071
Poisson Distribution and Its Application in Statistics......Page 1072
References and Further Reading......Page 1073
Poisson Processes on the Real Line......Page 1074
Poisson Processes on Abstract Spaces......Page 1075
Introduction......Page 1076
About the Author......Page 1077
Population Projections......Page 1078
Mean-Variance Analysis and its Justification......Page 1079
About the Author......Page 1080
Posterior Consistency in Bayesian Nonparametrics......Page 1081
References and Further Reading......Page 1082
About the Author......Page 1083
Reasons for Applying Data Preprocessing......Page 1084
Data Integration......Page 1085
References and Further Reading......Page 1086
Presenting the Data or Summary Tables That will be Analyzed......Page 1087
A Few Suggestions to Statisticians Desiring to Increase the Validity of and Weight Given to Statistical and Scientific Evidence......Page 1092
Cross References......Page 1094
An Example......Page 1095
How Many Components?......Page 1096
References and Further Reading......Page 1097
A Prototypical Policy Evaluation Problem......Page 1098
An Index Model of Choice and Treatment Effects: Definitions and Unifying Principles......Page 1099
Definitions of Treatment Effects in the Two Outcome Model......Page 1101
The Weights for a Generalized Roy Model......Page 1103
The Basic Principles Underlying the Identification of the Leading Econometric Evaluation Estimators......Page 1106
Matching......Page 1115
References and Further Reading......Page 1118
Results and Examples......Page 1120
Probabilistic Network Models......Page 1121
Introduction......Page 1122
Infinite Divisibility......Page 1123
Sources of Uncertainty in Statistics......Page 1124
The Kolmogorov Axioms......Page 1125
References and Further Reading......Page 1126
Probability, History of......Page 1127
About the Author......Page 1128
Introduction......Page 1129
Probit Model......Page 1130
Cross References......Page 1131
Promoting, Fostering and Development of Statistics in Developing Countries......Page 1132
Properties of Estimators......Page 1133
Cross References......Page 1135
Proportions, Inferences, and Comparisons......Page 1136
Psychiatry, Statistics in......Page 1137
Cross References......Page 1138
Cross References......Page 1139
The Null Hypothesis Significance Testing Controversy......Page 1140
About the Author......Page 1142
Public Opinion Polls......Page 1143
About the Author......Page 1144
P–Values......Page 1145
P-Values, Combining of......Page 1146
Pyramid Schemes......Page 1148
References and Further Reading......Page 1150
The Basic Set-Up: Risk Measures......Page 1152
Statistical Estimation......Page 1153
References and Further Reading......Page 1154
Questionnaire......Page 1155
Queueing Theory......Page 1157
References and Further Reading......Page 1159
R Language......Page 1160
2. Martingales.......Page 1162
7. The Radon–Nikodým derivative between two Markov jump processes.......Page 1163
References and Further Reading......Page 1164
Random Coefficient Models......Page 1165
Random Field......Page 1166
Basic Concepts......Page 1169
Limiting Properties of Eigenvectors......Page 1170
Set Partitions......Page 1171
Partition Processes and Partition Structures......Page 1172
Exchangeable Random Permutations......Page 1173
On the Number of Unseen Species......Page 1174
Equivariant Partition Models......Page 1175
Cluster Processes and Classification Models......Page 1176
References and Further Reading......Page 1177
Formal Definition......Page 1178
Random Walk......Page 1179
Randomization......Page 1181
Randomization Tests......Page 1183
References and Further Reading......Page 1184
RT-2......Page 1185
Introduction......Page 1186
Balanced Ranked Set Samples......Page 1187
References and Further Reading......Page 1188
Basic Formulations of the Ranking and Selection Problem......Page 1189
References and Further Reading......Page 1191
Augmented Ranking......Page 1192
Rao–Blackwell Theorem......Page 1193
References and Further Reading......Page 1194
Rating Scales......Page 1195
Definitions of Records......Page 1196
Sequential Ranks and Record Indicators......Page 1197
Distributions of Record Values......Page 1199
Cross References......Page 1201
References and Further Reading......Page 1202
Structure of a RP model......Page 1203
Learning the RP Model......Page 1204
Strengths and Weaknesses of RP Models......Page 1205
About the Author......Page 1206
Regression Diagnostics......Page 1207
About the Authors......Page 1208
Linear Regression Models......Page 1209
Estimation of Covariance Matrix......Page 1210
About the Author......Page 1211
Symmetrical Nonlinear Models......Page 1212
Introduction......Page 1213
References and Further Reading......Page 1214
Transformations......Page 1215
Internal Properties......Page 1216
Renewal Processes......Page 1218
References and Further Reading......Page 1221
References and Further Reading......Page 1222
Representative Samples......Page 1223
References and Further Reading......Page 1224
Factorial and Block Designs......Page 1225
Common Experimental Designs......Page 1226
Common Quasi-Experimental Designs......Page 1227
Residuals......Page 1228
About the Author......Page 1229
Response Surface Methodology......Page 1230
References and Further Reading......Page 1232
Ridge and Surrogate Ridge Regressions......Page 1233
Cross References......Page 1234
Education......Page 1235
Journals......Page 1236
Cross References......Page 1237
Likelihood......Page 1238
Recovery......Page 1239
References and Further Reading......Page 1240
Robust Inference......Page 1241
References and Further Reading......Page 1242
Diagnostic Measures......Page 1243
Cross References......Page 1244
Outliers......Page 1245
L Estimates......Page 1247
General Considerations......Page 1248
Introduction......Page 1249
The Breakdown Point......Page 1250
Heuristic Aspects of Robustness......Page 1251
ROC Curves......Page 1252
The Importance of Statistics......Page 1255
Statistics and Uncertainty......Page 1257
References and Further Reading......Page 1258
Statistics\' Role in Quantitative Education......Page 1259
Fundamental Understanding of the Scientific Method......Page 1260
Development/Enhancement of the Ability to Use the Higher-Order Analytic and Critical Thinking Skills Needed to Understand and C......Page 1261
References and Further Reading......Page 1262
Some Issues and Challenges Facing Developing Countries......Page 1263
Rubin Causal Model......Page 1264
About the Author......Page 1265
References and Further Reading......Page 1266
The Saddlepoint Approximation......Page 1268
Sample Size to Achieve a Given Variance or Relative Variance......Page 1270
Software for Sample Size Determination......Page 1271
Sample Survey Methods......Page 1272
Cross References......Page 1273
Sampling Algorithms......Page 1274
What is it?......Page 1275
Monte Carlo Simulations......Page 1277
Introduction......Page 1278
Systematic Sampling......Page 1279
Cluster and Multistage Sampling......Page 1280
About the Authors......Page 1281
Sampling Problems for Stochastic Processes......Page 1282
References and Further Reading......Page 1283
Scales of Measurement......Page 1284
Scales of Measurement and Distributional Assumptions......Page 1286
Rank Transformations and Appropriate Statistics......Page 1287
References and Further Reading......Page 1289
Seasonal Integration......Page 1290
Seasonal Cointegration......Page 1291
References and Further Reading......Page 1292
Seasonal Modeling......Page 1293
An Example......Page 1294
Selection of Appropriate Statistical Methods in Developing Countries......Page 1295
Cross References......Page 1296
References and Further Reading......Page 1297
Cross References......Page 1298
Use of Sensitivity Analysis......Page 1299
Design and Estimators......Page 1300
Variance-Based Sensitivity Measures......Page 1301
References and Further Reading......Page 1302
Sensometrics: Statistics, Psychometrics, or Chemometrics?......Page 1303
Example 2: Sensory Difference and Similarity Test Data......Page 1304
References and Further Reading......Page 1305
Introduction: Sequential Testing and Sequential Probability Ratios......Page 1306
Finite Termination and Average Sample Number (ASN)......Page 1307
About the Authors......Page 1308
Sequential Ranks......Page 1309
Cross References......Page 1311
Why Sequential Sampling?......Page 1312
Purely Sequential Sampling......Page 1313
Which Areas Are Hot Beds for Sequential Sampling?......Page 1314
Sex Ratio in National Birth Registers......Page 1315
References and Further Reading......Page 1316
Sign Test......Page 1317
References and Further Reading......Page 1318
The p-Value......Page 1319
Inversion of a Family of Tests to Obtain Confidence Regions......Page 1320
Cross References......Page 1321
Significance Tests, History and Logic of......Page 1322
References and Further Reading......Page 1323
The innumerable misuses of significance tests......Page 1324
Concluding Remarks......Page 1325
Simes\' Test in Multiple Testing......Page 1326
References and Further Reading......Page 1327
Simple Linear Regression......Page 1328
Simple Random Sample......Page 1329
Cross References......Page 1330
Simpson\'s Paradox......Page 1331
Simulation Based Bayes Procedures for Model Structures with Non-Elliptical Posteriors......Page 1333
References and Further Reading......Page 1335
Extensions of the Basic SSA......Page 1336
References and Further Reading......Page 1337
SIPOC and COPIS: Business Flow – Business Optimization Connection in a Six Sigma Context......Page 1338
References and Further Reading......Page 1339
The DMAIC Model......Page 1340
Skewness......Page 1341
Skew-Normal Distribution......Page 1343
Skew-Symmetric Families of Distributions......Page 1345
Introduction......Page 1347
Design-Based Methods......Page 1348
Unit Level Random Effects Model for Binary Data......Page 1349
Univariate Smoothing Splines......Page 1350
Splines on Riemannian Manifolds......Page 1351
References and Further Reading......Page 1353
Density Estimation......Page 1354
Additive Models......Page 1355
References and Further Reading......Page 1356
Exponential Random Graph Models......Page 1357
Longitudinal Models......Page 1358
Social Statistics......Page 1359
Introduction......Page 1360
Contingency Table Analysis......Page 1361
Introduction......Page 1362
About the Author......Page 1363
Geostatistics......Page 1364
Point Process Analysis and Random Sets......Page 1366
Lattice Data Analysis......Page 1367
References and Further Reading......Page 1368
Introduction......Page 1369
An Application......Page 1370
References and Further Reading......Page 1371
Sport, Statistics in......Page 1372
About the Authors......Page 1373
Spreadsheets in Statistics......Page 1374
Spurious Correlation......Page 1375
About the Author......Page 1377
St. Petersburg Paradox......Page 1378
Definition......Page 1379
References and Further Reading......Page 1380
Drug Release from Pharmaceutical Systems......Page 1381
Defining the Statistical Problem......Page 1382
Introduction......Page 1384
Generalized Estimating Equations Models......Page 1385
About the Author......Page 1386
Statistical Approaches to Protecting Confidentiality in Public Use Data......Page 1387
References and Further Reading......Page 1388
References and Further Reading......Page 1390
Desirable Qualities for a Statistical Consultant......Page 1391
Cross References......Page 1392
Optimal Designs......Page 1393
Factorial Designs......Page 1394
Fractional Factorial Designs of the Type 2k-p......Page 1395
References and Further Reading......Page 1396
Discrete Distributions......Page 1397
Continuous Distributions......Page 1398
Moments and Other Measures......Page 1399
Cross References......Page 1401
Distance Sampling......Page 1402
Future......Page 1403
References and Further Reading......Page 1404
Empirical Estimation of......Page 1405
Cross References......Page 1406
Statistical Evidence......Page 1407
Cross References......Page 1409
Statistical Fallacies......Page 1410
References and Further Reading......Page 1412
Statistical Fallacies: Misconceptions, and Myths......Page 1413
References and Further Reading......Page 1417
Statistical Genetics......Page 1418
Statistical Inference......Page 1419
Statistical Inference for Quantum Systems......Page 1421
Cross References......Page 1423
Markov Chains and Sequences......Page 1424
Bienayme-Galton-Watson Branching Process......Page 1425
Non-parametric Modeling Based on Functional Estimation......Page 1426
Counting and Pure Jump Markov Processes......Page 1427
Diffusion Processes......Page 1428
Efficiency of Estimators......Page 1429
References and Further Reading......Page 1430
Statistical Inference in Ecology......Page 1431
References and Further Reading......Page 1433
Frequentist Statistical Inference......Page 1434
Different Forms of Statistical Inference......Page 1435
Bayesian Inference......Page 1438
References and Further Reading......Page 1439
Statistical Literacy, Reasoning, and Thinking......Page 1440
Words That Characterize Assessment Items for Statistical Literacy, Reasoning, and Thinking......Page 1441
References and Further Reading......Page 1442
Characterizing Functions of Non-Precise Data......Page 1443
About the Author......Page 1444
Cohort Studies......Page 1445
Regression vs. Non-Regression Methods......Page 1447
Overview......Page 1448
Black–Scholes Model......Page 1449
Conclusions......Page 1450
Statistical Modelling in Market Research......Page 1451
Statistical Natural Language Processing......Page 1453
Problem Description......Page 1454
Applicant Recognition for Project Realization with Good Contract Risk......Page 1455
Signal Detection in Clutter......Page 1456
References and Further Reading......Page 1458
Statistical Publications, History of......Page 1459
Quality: A Brief Introduction......Page 1460
Usual Statistical Techniques in SQC......Page 1461
References and Further Reading......Page 1463
Univariate Control Charts Versus Multivariate Control Charts......Page 1464
SPC Applications in Service Industries......Page 1465
References and Further Reading......Page 1466
Statistical Signal Processing......Page 1467
Array Model......Page 1468
Statistical Significance......Page 1469
Cross References......Page 1470
BMDP, SAS, SPSS......Page 1471
S, LISP-STAT, R......Page 1472
About the Author......Page 1473
Statistical View of Information Theory......Page 1474
Acknowledgment......Page 1475
What Is Needed?......Page 1476
Some Working Initiatives......Page 1477
Introduction......Page 1478
Bold Play in Red and Black......Page 1479
Statistics and the Law......Page 1480
References and Further Reading......Page 1482
University Education in Statistics......Page 1483
Statistics in the Workplace......Page 1484
Introduction......Page 1485
Threshold Exceedances......Page 1486
Further Reading......Page 1487
Introduction......Page 1488
Distance between Ranked Lists......Page 1489
Aggregation of Ranked Lists......Page 1490
Cross Reference......Page 1491
Statistics, Targeted Clinical Trials,and Stratified Medicine......Page 1492
Cross References......Page 1493
Staatswissenschaft and Political Arithmetic......Page 1494
Statistics and the Statistical Method: The Theory of Errors......Page 1495
Jakob Bernoulli, De Moivre, Bayes: Chance and Design......Page 1496
The Theory of Probability and Statistics: Quetelet......Page 1498
New Times: Great Progress and the Soviet cul-de-sac......Page 1499
The Two Streams of Statistical Thought......Page 1501
References and Further Reading......Page 1502
Statistics: An Overview......Page 1505
References and Further Reading......Page 1509
Example 3: Placeboes in Surgery......Page 1510
Statistical Science is a Wonderful Subject......Page 1511
The Experimental Cycle......Page 1512
Cross References......Page 1513
Stem-and-Leaf Plot......Page 1514
Introduction......Page 1515
The Cumulative Exposure Model......Page 1516
Cross References......Page 1517
Stochastic Difference Equations and Applications......Page 1518
References and Further Reading......Page 1520
Stochastic Differential Equations......Page 1521
Stochastic Global Optimization......Page 1522
References and Further Reading......Page 1524
Modeling by Stochastic Differential Equations......Page 1525
References and Further Reading......Page 1526
Stochastic Modeling Analysis and Applications......Page 1527
Random Walk Modeling Approach (Ladde and Ladde ch571:ladde2009)......Page 1528
Sequential Colored Noise Modeling Approach (Ladde and Ladde ch571:ladde2009; Wong ch571:wong1971)......Page 1530
Cross References......Page 1531
Stochastic Models of Transport Processes......Page 1532
References and Further Reading......Page 1534
Definition of a Stochastic Process......Page 1535
Construction of Canonical Processes......Page 1536
Series Expansion in L2......Page 1537
Extensions of the Theory......Page 1538
Cross References......Page 1539
Martingales in Finance......Page 1540
Insurance Risk Model......Page 1541
Definitions......Page 1542
State and Time Discretized Process......Page 1543
Markov Chains......Page 1544
Birth and Death Process......Page 1545
Martingale Process......Page 1546
About the Author......Page 1547
Estimation Under Simple Random Sampling Within Strata......Page 1548
Variance Estimation for Stratified Samples......Page 1549
Controlled Selection......Page 1550
Strong Approximations in Probability and Statistics......Page 1551
Mathematical Representation......Page 1553
Model Estimation......Page 1554
Equivalent Structural Equation Models......Page 1555
Introduction......Page 1556
State Space Form......Page 1557
References and Further Reading......Page 1558
Student\'s t-Distribution......Page 1559
Introduction......Page 1560
One-Sample t-Test......Page 1561
Two Independent Samples......Page 1562
References and Further Reading......Page 1563
Histogram as Density Estimator......Page 1564
The Rules in Practice......Page 1565
About the Author......Page 1566
One-Parameter Case......Page 1567
Multi-Parameter Case......Page 1568
Cross References......Page 1569
Neyman Factorization......Page 1570
A Complete Sufficient Statistic......Page 1571
References and Further Reading......Page 1572
Varied Versions of the Basic Boxplot......Page 1573
Outlier Rule......Page 1574
References and Further Reading......Page 1575
Superpopulation Models in Survey Sampling......Page 1576
References and Further Reading......Page 1577
Overviews......Page 1578
Complex Situations......Page 1579
References and Further Reading......Page 1580
Statistical Analysis......Page 1581
About the Author......Page 1582
References and Further Reading......Page 1583
von Mises Expansions of Target Functionals......Page 1584
Final Remarks......Page 1585
Telephone Sampling: Frames and Selection Techniques......Page 1586
References and Further Reading......Page 1587
Asymptotically Linear Statistics......Page 1588
Distribution Free Versions of Empirical Processes......Page 1589
Cross References......Page 1590
Introduction......Page 1591
Similar and Location-Invariant Tests......Page 1592
Introduction......Page 1593
Alternative Approaches......Page 1594
References and Further Reading......Page 1595
Tests for Equality of Variances of k Populations......Page 1596
References and Further Reading......Page 1597
The Probability Integral Transformation......Page 1598
Testing for Interdependence......Page 1599
About the Author......Page 1601
Time Series......Page 1602
Acknowledgments......Page 1605
Time Series Models to Determine the Death Rate of a Given Disease......Page 1606
About the Author......Page 1607
Regression with Autocorrelated Errors......Page 1608
Regression with Heteroscedasticity......Page 1609
References and Further Reading......Page 1610
Total Survey Error......Page 1611
Tourism Statistics......Page 1613
Two-Stage Least Squares......Page 1617
Trend Estimation......Page 1614
References and Further Reading......Page 1619
Unbiased Estimators and Their Applications......Page 1620
Properties of the Uniform Distribution......Page 1622
Uniform Distribution and Modelingof Random Variables......Page 1623
Uniform Experimental Design......Page 1624
References and Further Reading......Page 1625
Algorithmic Generators......Page 1626
Multivariate Uniformity......Page 1627
Linear recurrences modulo m......Page 1628
Recommendations......Page 1629
References and Further Reading......Page 1630
Historical Perspective......Page 1631
Properties......Page 1633
References and Further Reading......Page 1634
U-Statistics......Page 1635
References and Further Reading......Page 1636
Validity of Scales......Page 1638
References and Further Reading......Page 1639
Cross References......Page 1640
Variance......Page 1641
Nominal Case......Page 1643
Ordinal Case......Page 1644
About the Author......Page 1645
The Model Setup......Page 1646
Extensions......Page 1647
References and Further Reading......Page 1648
Some Typical Roles of Weak Convergence in Probability......Page 1650
Relative Compactness, Tightness and Prohorov\'s Theorem......Page 1651
Weibull Distribution......Page 1652
Introduction......Page 1654
A New Way of Developing Weighted Correlation Coefficients......Page 1655
Weighted U-Statistics......Page 1656
Wilcoxon–Mann–Whitney Test......Page 1657
References and Further Reading......Page 1658
Wilcoxon-Signed-Rank Test......Page 1659
References and Further Reading......Page 1660
List of Entries......Page 1662