International encyclopedia of statistical science

Absolute Penalty Estimation......Page 1
References and Further Reading......Page 2
Accelerated Lifetime Testing......Page 3
References and Further Reading......Page 4
Factors for Classifications of Sampling Plans......Page 5
A Few Characteristics of a Sampling Plan......Page 6
Actuarial Methods......Page 7
Key Terms......Page 8
Cross References......Page 9
Adaptive Linear Regression......Page 10
What Is Adaptivity?......Page 12
Cross References......Page 13
Adaptive Sampling......Page 14
About the Author......Page 15
Ranking......Page 16
Estimating the CDF or Histogram......Page 17
References and Further Reading......Page 18
African Population Censuses......Page 19
Aggregation Schemes......Page 20
References and Further Reading......Page 22
Agriculture, Statistics in......Page 23
About the Author......Page 24
Cross References......Page 25
Background......Page 26
Derivation......Page 27
Refinements......Page 28
Algebraic Statistics......Page 29
Algebraic Statistics for Contingency Tables......Page 30
References and Further Reading......Page 31
Important Almost Sure Convergence Theorems......Page 32
References and Further Reading......Page 34
Spatial Correlation Measures......Page 35
Spatial Linear Regression......Page 36
Spatial Interaction Data......Page 37
References and Further Reading......Page 38
Purpose of ANCOVA......Page 39
Alternatives to ANCOVA......Page 40
Analysis of Multivariate Agricultural Data......Page 41
References and Further Reading......Page 43
One-Way Analysis of Variance......Page 44
The normalnormalF-Test......Page 45
Introduction......Page 46
Departures from Equal Variances......Page 47
Tests for Normality......Page 48
Transformations to Correct Lack of Homoscedasticity......Page 49
References and Further Reading......Page 50
Outline of Derivation......Page 52
Anderson–Darling Tests with Unknown Parameters......Page 53
Introduction......Page 54
Approximations to the Densities of Sufficient Estimators......Page 55
Introduction......Page 57
Curve Fitting......Page 58
Asymptotic Expansions......Page 59
Attitudes and Perspectives......Page 60
Symmetric Measures......Page 61
Asymmetric Measures......Page 62
Concluding Comment......Page 63
History......Page 64
Censoring and Truncation......Page 65
References and Further Reading......Page 66
Asymptotic Normality......Page 67
Definition in the General Case......Page 68
A Compromise: The Hodges–Lehmann Location Estimator......Page 69
Fixed Width Confidence Intervals and ARE......Page 70
Cross References......Page 71
Asymptotic Relative Efficiency of Two Tests......Page 72
Bahadur Efficiency......Page 73
References and Further Reading......Page 74
References and Further Reading......Page 75
Autocorrelation in Regression......Page 76
Ingredients of Probability Spaces......Page 77
Axioms of Probability......Page 78
References and Further Reading......Page 79
Cross References......Page 80
Statistics in Banking: The Colombian Perspective......Page 81
References and Further Reading......Page 82
Bartlett Correction......Page 83
Bartlett-Type Correction......Page 84
References and Further Reading......Page 85
Bartlett's Test......Page 86
References and Further Reading......Page 87
About the Author......Page 88
The Economist 2000......Page 89
Laplace and Venn......Page 90
Priors and Priors......Page 91
Lindley and Territory......Page 92
Curvature: The Bane of Bayes......Page 93
Why Bayes?......Page 94
References and Further Reading......Page 95
Bayesian Approach of the Unit Root Test......Page 96
Conclusions......Page 97
Bayesian Nonparametric Statistics......Page 98
References and Further Reading......Page 99
Bayesian P-Values......Page 100
About the Authors......Page 102
Bayesian Reliability Modeling......Page 103
References and Further Reading......Page 104
Observation Models......Page 105
Introduction......Page 106
Probability as a Measure of Conditional Uncertainty......Page 108
Statistical Inference and Decision Theory......Page 109
Exchangeability and Representation Theorem......Page 110
The Bayesian Paradigm......Page 111
The Learning Process......Page 112
Predictive Distributions......Page 115
Asymptotic Behavior......Page 116
Inference Summaries......Page 117
Estimation......Page 118
Hypothesis Testing......Page 120
Reference Analysis......Page 122
Reference Distributions......Page 123
Frequentist Properties......Page 127
Objectivity......Page 129
Applicability......Page 130
References and Further Reading......Page 131
Bayesian Statistics......Page 132
Why to Become Frequentist/Bayesian?......Page 133
References and Further Reading......Page 134
Bayesian vs. Classical Point Estimation: A Comparative Overview......Page 135
Introduction......Page 137
Other Solutions......Page 138
References and Further Reading......Page 139
The Best Linear Unbiased Estimator (BLUE) of Xbold0mu mumu No Author Given......Page 140
Two Linear Models......Page 141
About the Authors......Page 142
Beta Distribution......Page 143
Bias Analysis......Page 144
Confounding......Page 145
References and Further Reading......Page 146
Introduction......Page 147
General Formula......Page 148
Binomial Distribution......Page 151
Bioinformatics......Page 153
References and Further Reading......Page 154
Biopharmaceutical Research, Statistics in......Page 155
About the Author......Page 156
Biostatistics......Page 157
Continuous Bivariate Distributions......Page 159
Discrete Bivariate Distributions......Page 162
Dependence......Page 163
Bootstrap Asymptotics......Page 165
References and Further Reading......Page 167
The Basic Idea......Page 168
Extension to Dependent Data......Page 169
When and Why Bootstrap Can Fail to Work......Page 170
About the Authors......Page 171
References and Further Reading......Page 172
The Borel–Cantelli Lemma......Page 173
Generalizations......Page 174
Box–Cox Transformation......Page 175
Autocorrelation and Partial Autocorrelation Functions......Page 177
About the Author......Page 179
Brownian Motion and the Wiener Process......Page 180
Semigroups Associated with Markov Transition Probability Functions......Page 182
Forecasting, Planning, and Goals......Page 184
Time Series Methods......Page 185
References and Further Reading......Page 186
Business Intelligence......Page 187
An Overview and Definitions......Page 188
The Future of Business Statistics Education......Page 189
Business Surveys......Page 190
References and Further Reading......Page 193
Calibration......Page 194
Introduction......Page 195
 Measures of Association......Page 196
Cross References......Page 197
Procedure......Page 198
Interpretation......Page 199
Careers in Statistics......Page 200
Medicine......Page 201
Cross References......Page 202
Types of Case-Control Studies......Page 203
References and Further Reading......Page 204
Contingency Tables......Page 205
References and Further Reading......Page 206
Basics of Graph Theory......Page 207
Interpretations of Graphs......Page 208
Control: Manipulation Versus Conditioning......Page 209
Separation......Page 210
Bias and Confounding......Page 211
Estimation of Causal Effects......Page 212
Questions of Discovery......Page 213
References and Further Reading......Page 214
Counterfactuals and Potential Outcomes......Page 215
From Randomized to Observational Inference......Page 216
Canonical Inference......Page 217
Cross References......Page 218
References and Further Reading......Page 219
Basic Concepts on Censored Data......Page 220
Type-II Censoring......Page 221
Cross References......Page 222
History......Page 223
Planning the Census......Page 224
Collecting the Information......Page 225
Problems in Census Taking and Issues for the Future......Page 226
Introduction......Page 227
Different Versions of the Central Limit Theorem......Page 228
Rates of Convergence to Normality......Page 230
Asymptotic Distributions of Statistics not Expressible as Sums of Random Variables......Page 231
Central Limit Theorems for Stochastic Processes......Page 232
Chaotic Modelling......Page 233
References and Further Reading......Page 236
Characteristic Functions......Page 237
Chebyshev's Inequality......Page 238
Chemometrics......Page 239
References and Further Reading......Page 240
Cross References......Page 241
Chernoff Faces......Page 242
About the Author......Page 243
Chi-Square Distribution......Page 244
Chi-Square Goodness-of-Fit Tests: Drawbacks and Improvements......Page 245
References and Further Reading......Page 248
Likelihood Ratio Chi-Square......Page 249
Summary......Page 250
Chi-Square Tests......Page 251
References and Further Reading......Page 252
Clinical Trials, History of......Page 253
References and Further Reading......Page 254
Clinical Trials: An Overview......Page 255
Side Effect of Drugs......Page 258
Large Clinical Trials: Meta-analysis......Page 259
About the Author......Page 260
Cluster Analysis: An Introduction......Page 261
Cluster Sampling......Page 264
Collapsibility in Contingency Tables......Page 266
Collapsibility in Regression Models......Page 267
References and Further Reading......Page 268
Comparability: Definition and Assessment......Page 269
Comparability in Official Statistics......Page 270
References and Further Reading......Page 271
Complier-Average Causal Effect (CACE) Estimation......Page 272
About the Author......Page 273
Composite Indicators......Page 274
What Is Computational Statistics?......Page 275
Symbolic/Exact Methods......Page 276
Future Directions......Page 277
Conditional Expectation and Probability......Page 278
Confidence Distributions......Page 281
Confidence Interval......Page 282
Introduction......Page 283
The Potential-Outcome Model of Confounding......Page 284
Confounders (Confounding Factors) and Covariate Imbalance......Page 285
Adjustment for Confounding......Page 286
Confounder Selection......Page 287
References and Further Reading......Page 288
Contagious Distributions......Page 289
References and Further Reading......Page 290
Continuity Correction......Page 291
Introduction......Page 292
Some Modifications of the Basic Chart......Page 293
Some Other Types of Control Charts......Page 294
EWMA Charts......Page 295
Introduction......Page 296
Convergence in Probability......Page 297
Almost Sure Convergence......Page 298
References and Further Reading......Page 299
Cook's Distance......Page 300
Copulas......Page 301
References and Further Reading......Page 303
Pricing Applications......Page 304
Risk Management......Page 305
Copulas and Temporal Dependence in Finance......Page 306
Financial Prices Dynamics and Copulas......Page 307
Dependence......Page 308
Copulas......Page 309
Acknowledgments......Page 310
Introduction......Page 311
Expansion Formulas......Page 312
Error Bounds......Page 313
Population Correlation Coefficient......Page 314
A Sample Correlation Coefficient......Page 315
Partial Correlations......Page 316
Correspondence Analysis......Page 317
References and Further Reading......Page 319
References and Further Reading......Page 320
Cramér–Rao and UMVUE......Page 321
Introduction......Page 322
All Parameters Known......Page 323
About the Author......Page 324
The Basic Multilevel Model......Page 325
About the Author......Page 326
Cross-Covariance Operators......Page 327
References and Further Reading......Page 328
The Development of Data Analysis......Page 329
The Techniques of Data Analysis......Page 330
Three-Way Data Analysis......Page 331
Data Depth......Page 332
Data Mining......Page 334
References and Further Reading......Page 336
Data Mining Time Series Data......Page 337
Time Series Representations......Page 338
References and Further Reading......Page 339
Introduction......Page 340
Computer Science Approaches......Page 341
References and Further Reading......Page 342
Introduction and Summary......Page 343
Decision Theory: An Introduction......Page 344
Decision Theory: An Overview......Page 347
Decision Matrices......Page 348
Probability or Uncertainty......Page 349
The Maximax Rule......Page 350
Expected Utility......Page 351
Ellsberg's Paradox......Page 352
References and Further Reading......Page 353
Example......Page 354
Dynamic Regression Models......Page 357
Modeling of Degradation Process......Page 358
Degrees of Freedom......Page 361
DF in Terms of Dimensions and Parameters......Page 362
Degrees of Freedom in Statistical Inference......Page 363
About the Author......Page 364
Macro-Level Focus......Page 365
Micro-Level Processes......Page 366
References and Further Reading......Page 367
Demographic Data......Page 368
Data Cleaning and Careful Description......Page 369
References and Further Reading......Page 370
Density Ratio Model......Page 371
Design for Six Sigma......Page 372
Design of Experiments: A Pattern of Progress......Page 374
Introduction......Page 375
Choice of Design for GLMs......Page 376
References and Further Reading......Page 377
Detecting Outliers of a Simulated normalnormalAR(1) Time Series......Page 378
Simulation of Simultaneous Transfer Function (STF) Model......Page 379
Turns in Business Cycles......Page 380
Models......Page 381
References and Further Reading......Page 382
Dickey-Fuller Tests......Page 383
Discriminant Analysis: An Overview......Page 386
PDA Versus DDA......Page 388
More Issues and Problems......Page 389
Introduction......Page 390
Exponential Dispersion Models......Page 391
Tweedie Exponential Dispersion Models......Page 393
References and Further Reading......Page 394
Distance Measures......Page 395
Distance Sampling......Page 396
About the Authors......Page 397
Geometric Distribution of Order normalnormalk......Page 398
Binomial Distribution of Order normalnormalk......Page 399
Introduction......Page 400
Cardinal Measures......Page 401
Statistical Inferences......Page 402
Divisible Statistics......Page 403
Dummy Variables......Page 405
Durbin–Watson Test......Page 406
References and Further Reading......Page 407
Econometrics......Page 408
References and Further Reading......Page 409
About the Author......Page 411
Misuse of Certain Statistics......Page 412
About the Author......Page 413
Sample Surveys......Page 414
System of National Accounts......Page 415
An Example......Page 416
About the Author......Page 417
Formal Expansion......Page 418
Cornish–Fisher EE......Page 419
Effect Modification and Biological Interaction......Page 420
Biological Interaction......Page 421
References and Further Reading......Page 422
Effect Size......Page 423
References and Further Reading......Page 425
Eigenvalue, Eigenvector and Eigenspace......Page 426
References and Further Reading......Page 427
Empirical Likelihood: IID Case......Page 428
Pseudo-EL: Complex Surveys......Page 429
Empirical Processes......Page 430
References and Further Reading......Page 432
Properties of H......Page 433
Cross-Entropy (Divergence)......Page 434
Parameterized Generalizations......Page 435
References and Further Reading......Page 436
Entropy Functional......Page 437
ANODIV......Page 438
Characterization......Page 439
Some Applications of CE......Page 440
About the Author......Page 441
References and Further Reading......Page 442
Environmental Monitoring, Statistics Role in......Page 443
Equivalence Testing......Page 444
Birkhoff's Ergodic Theorem......Page 446
Kingman's Subadditive Ergodic Theorem......Page 447
Erlang's Formulas......Page 448
First Erlang Formula......Page 449
Exact Decomposition Formulas for the Multi-Server Erlang Loss-Delay Queue......Page 450
References and Further Reading......Page 451
Introduction......Page 452
Defining Point Estimators......Page 453
Evaluating Point Estimators......Page 454
References and Further Reading......Page 455
Estimation Problems for Random Fields......Page 456
How to Construct Estimators?......Page 457
The Plug in Principle......Page 458
M-Estimators......Page 459
About the Author......Page 460
Responsibilities......Page 461
About the Author......Page 462
Different Observation Plans......Page 463
Censoring......Page 464
Parallel and Interdependent Processes......Page 465
References and Further Reading......Page 466
Introduction and Simple Case......Page 467
Composite Case: Non-Group Model......Page 468
Exact Inference for Categorical Data......Page 469
Ibold0mu mumu No Author GivenJ Tables......Page 470
Exchangeability......Page 471
About the Authors......Page 472
Computing Rules......Page 473
References and Further Reading......Page 474
Components of Experimental Design......Page 475
Cross References......Page 476
Expert Systems......Page 477
Introduction......Page 479
 Same Data, Different Methods, Different Outcomes......Page 480
Conclusion......Page 482
Exploratory Data Analysis......Page 483
About the Author......Page 484
Exponential and Holt-Winters 
Smoothing......Page 485
Exponential Family Models......Page 487
References and Further Reading......Page 489
Introduction......Page 490
Extreme Value Theory and Max-Stability......Page 491
Extremes of Gaussian Processes......Page 493
References and Further Reading......Page 495
Definition of the F Distribution......Page 496
On Numerical Computations......Page 497
Background......Page 498
The Literature......Page 499
Factorial Experiments......Page 500
Multiple Hypothesis Testing......Page 501
Mathematical Definitions......Page 502
Control and Estimation......Page 503
About the Author......Page 504
Introduction......Page 505
Mother–Baby Structures......Page 506
Analytical Options......Page 507
Stability Analysis......Page 508
References and Further Reading......Page 510
Ongoing and Upcoming Issues......Page 511
Introduction......Page 512
Generalized Fiducial Distribution......Page 513
Examples......Page 514
References and Further Reading......Page 515
Financial Return Distributions......Page 516
References and Further Reading......Page 517
First Exit Time Problem......Page 518
References and Further Reading......Page 519
Analytical Time Scale......Page 520
Fisher Exact Test......Page 521
Fisher-Tippett Theorem......Page 522
Five-Number Summaries......Page 523
Forecasting Methods......Page 524
Forecasting Canon......Page 528
Be Conservative When Uncertain......Page 530
Forecasting with ARIMA Processes......Page 531
Computation of Forecasts......Page 532
What Can Be Forecast?......Page 533
The Basic Steps in a Forecasting Task......Page 534
Percentage Errors......Page 535
Introduction......Page 536
Paternity Determination......Page 537
References and Further Reading......Page 538
Kolmorgorov's Axioms......Page 539
References and Further Reading......Page 540
Frailty Model......Page 541
References and Further Reading......Page 542
Fraud in Statistics......Page 543
Frequentist Hypothesis Testing: A Defense......Page 544
Cross References......Page 547
Introduction......Page 548
FBST Definition......Page 549
Cross References......Page 550
Functional Data Analysis......Page 551
Introduction......Page 552
Functional Derivatives......Page 553
Statistical Functionals and the Bootstrap......Page 554
Probability and Statistics with Fuzziness......Page 555
Fuzzy Clustering and Classification......Page 556
Fuzzy Principal Component Analysis......Page 557
Statistical Hypothesis Tests and Confidence Intervals......Page 558
References and Further Reading......Page 559
Fuzzy Set Theory and Probability Theory: What is the Relationship?......Page 560
References and Further Reading......Page 562
Definitions......Page 563
The Algebra of Fuzzy Subsets......Page 564
Explanation......Page 565
Preliminary......Page 566
References and Further Reading......Page 567
Properties of Estimators......Page 569
Cross References......Page 570
Gaussian Processes......Page 571
About the Author......Page 572
Gauss-Markov Theorem......Page 573
Historical Notes......Page 574
References and Further Reading......Page 576
General Linear Models......Page 578
References and Further Reading......Page 580
Generalized Extreme Value Family of Probability Distributions......Page 581
Cumulative Distribution Function......Page 582
References and Further Reading......Page 583
Generalized Hyperbolic Distributions......Page 585
References and Further Reading......Page 586
Theory......Page 587
Goodness-of-Fit......Page 590
Application......Page 591
References and Further Reading......Page 592
Illustration for the Binary Case......Page 593
GQL Estimation: A Generalization of the QL Estimation to the Correlated Data......Page 594
Generalized Rayleigh Distribution......Page 595
References and Further Reading......Page 598
Generalizations......Page 599
About the Author......Page 600
Introduction......Page 601
Properties......Page 602
About the Author......Page 603
Geometric Mean......Page 604
Kriging Predictions......Page 605
Block Kriging......Page 606
About the Author......Page 607
Generalizations of Glivenko-Cantelli Theorem......Page 608
A Simple Comparative Experiment......Page 610
A Split Plot Experiment......Page 611
About the Author......Page 613
Graphical Markov Models......Page 614
References and Further Reading......Page 616
Nonresponse in Ranked Set Sampling......Page 617
Harmonic Mean......Page 618
Cross References......Page 619
Cross References......Page 620
Cox Regression Model......Page 621
Definition of HTD......Page 622
Remarks......Page 623
Heteroscedastic Time Series......Page 624
Introduction......Page 626
Detection of Heteroscedasticity......Page 627
Remedial Measures......Page 628
References and Further Reading......Page 629
About the Author......Page 630
Hodges-Lehmann Estimators......Page 631
References and Further Reading......Page 632
Properties of the H–T Estimator......Page 633
References and Further Reading......Page 634
Hyperbolic Secant Distributions and Generalizations......Page 636
Hypergeometric Distribution and Its Application in Statistics......Page 637
References and Further Reading......Page 639
Overview......Page 640
Applications in Statistics and Decision Theory......Page 641
About the Authors......Page 642
References and Further Reading......Page 643
Applications......Page 644
Imputation......Page 645
References and Further Reading......Page 647
IBDs with High Efficiency Factors......Page 648
Some Applications of IBDs......Page 649
Incomplete Data in Clinical and Epidemiological Studies......Page 650
Definition......Page 651
The Jevons Index......Page 652
The Fisher Index......Page 653
Areas of Research......Page 654
Control Charts......Page 655
Six Sigma......Page 656
Inference Under Informative Probability Sampling......Page 657
References and Further Reading......Page 659
References and Further Reading......Page 660
About the Author......Page 661
Instrumental Variables......Page 662
Insurance, Statistics in......Page 664
Integrated Statistical Databases......Page 666
Interaction......Page 668
Interactive and Dynamic Statistical Graphics......Page 669
Main Concepts of Interactive and Dynamic Statistical Graphics......Page 670
Software for Interactive and Dynamic Statistical Graphics......Page 671
An Interactive Graphical Example......Page 672
Further Reading and Viewing......Page 673
Internet Survey Methodology: Recent Trends and Developments......Page 674
References and Further Reading......Page 676
Intervention Model......Page 677
References and Further Reading......Page 679
Intraclass Correlation Coefficient......Page 680
Characteristics of IG Distribution......Page 682
Inverse Sampling......Page 683
Inversion of Bayes' Formula for Events......Page 685
Cross References......Page 689
Itô Integral......Page 690
References and Further Reading......Page 691
Variance Estimation......Page 692
References and Further Reading......Page 693
James–Stein Estimator in the Original Problem......Page 694
References and Further Reading......Page 695
Testing Normality of Unobserved Regression Residuals......Page 696
Jump Regression Analysis......Page 697
2-D Jump Regression Analysis......Page 698
References and Further Reading......Page 699
Kalman Filtering......Page 700
Implementation Methods......Page 701
References and Further Reading......Page 703
Kaplan-Meier Estimator......Page 704
Introduction......Page 705
Specific Category Kappa......Page 706
Statistical Inferences......Page 707
Kendall's Tau......Page 708
Kendall's Tau-b......Page 709
Background......Page 710
Khmaladze Transformation......Page 711
Cross References......Page 712
Kolmogorov-Smirnov Test......Page 713
Kullback-Leibler Divergence......Page 715
References and Further Reading......Page 716
Kurtosis: An Overview......Page 717
References and Further Reading......Page 718
Large Deviations and Applications......Page 719
Laws of Large Numbers......Page 720
Cross References......Page 722
My SQU Experience......Page 723
Least Absolute Residuals Procedure......Page 724
References and Further Reading......Page 725
Least Squares......Page 726
Introduction......Page 727
The Variance Gamma Process......Page 728
Life Expectancy......Page 729
References and Further Reading......Page 730
Life Table......Page 731
Introduction......Page 732
Inference......Page 733
Extensions to Likelihood......Page 734
References and Further Reading......Page 735
Limit Theorems of Probability Theory......Page 736
Linear Mixed Models......Page 738
About the Author......Page 739
Aspects of Data, Model and Notation......Page 740
Background......Page 741
Algebraic Properties of Least Squares......Page 742
Comparing Two Basic Linear Regression Models......Page 743
References and Further Reading......Page 744
Local Asymptotic Mixed Normal Family......Page 745
Location-Scale Distributions......Page 746
About the Author......Page 747
References and Further Reading......Page 748
Logistic Regression......Page 749
Logistic Distribution......Page 752
Definition and Properties......Page 754
About the Author......Page 755
Loss Function......Page 756
References and Further Reading......Page 757
Definition......Page 758
Intrinsic Priors for Model Selection and Hypothesis Testing......Page 759
Marine Research, Statistics in......Page 760
Cross References......Page 761
Introduction......Page 762
Metropolis–Hastings method......Page 763
About the Author......Page 764
Introduction......Page 765
Discrete Time Markov Chains......Page 766
Markov Chains and Markov Processes......Page 767
Markov Processes......Page 768
Cross References......Page 769
Martingale Central Limit Theorem......Page 770
References and Further Reading......Page 771
Martingales......Page 772
References and Further Reading......Page 773
Introduction......Page 774
Atmospheric Temperature, Ta......Page 775
Parametric Analysis......Page 776
A Differential Equation of CO2 in the Atmosphere......Page 777
References and Further Reading......Page 778
Maximum Entropy Method for Estimation of Missing Data......Page 779
Mean, Median and Mode......Page 780
Introduction......Page 781
The Median......Page 782
The Mode......Page 783
Mean Residual Life......Page 784
References and Further Reading......Page 785
Foundations of Probability: Fields and Sigma-Fields......Page 786
Integration......Page 787
Parts of MEM......Page 788
Functional Method: Corrected Score......Page 789
Nonparametric Estimation......Page 790
Measurement of Economic Progress......Page 791
References and Further Reading......Page 792
Measurement of Uncertainty......Page 793
References and Further Reading......Page 795
Measures of Agreement......Page 796
Measures of Dependence......Page 797
References and Further Reading......Page 798
References and Further Reading......Page 799
Clinical Trials......Page 800
References and Further Reading......Page 801
Illustrative Methodological Developments......Page 802
Conclusion......Page 803
Introduction......Page 804
Qualitative Grounds......Page 805
Inference for the REM......Page 806
References and Further Reading......Page 807
Method Comparison Studies......Page 808
Methods of Moments Estimation......Page 809
Minimum Variance Unbiased......Page 810
So What Is Statistics?......Page 812
References and Further Reading......Page 813
Misuse of Statistics......Page 814
References and Further Reading......Page 816
Early Developments......Page 817
Relationship to Other Methods of Multivariate Analysis......Page 818
References and Further Reading......Page 819
Statistical Problems......Page 820
EM Algorithm......Page 821
References and Further Reading......Page 822
Bayesian Approach......Page 823
Model Selection in High Dimensional Models......Page 824
References and Further Reading......Page 825
Stochastic Models for Spatial Data......Page 826
Bayesian Kriging......Page 827
Generalized Linear Geostatistical Models......Page 828
Modeling Count Data......Page 829
Modeling Randomness Using System Dynamics Concepts......Page 832
Modeling Survival Data......Page 834
About the Author......Page 836
First construction......Page 837
Fourth Construction......Page 838
About the Author......Page 839
Moderate Deviations......Page 840
Moderating and Mediating Variables in Psychological Research......Page 842
Moment Generating Function......Page 845
The Basic Monte Carlo Principle and Its Extensions......Page 847
MCMC Methods......Page 848
Some Uses of Monte Carlo in Statistics......Page 849
About the Author......Page 850
Introduction......Page 851
Starting Point......Page 852
Three Monty Hall Problems......Page 853
Answer to Marilyn Vos Savant's Q-0: Should You Switch Doors?......Page 854
Discussion......Page 855
About the Authors......Page 856
Neyman-Pearson Theory......Page 857
Invariant and Unbiased Tests......Page 858
Smoothing Using Two-Sided Moving Averages......Page 859
Centered Moving Averages......Page 860
Moving Average Processes......Page 861
Multicollinearity......Page 862
Usual Clustering Problems......Page 863
Modified Agglomerative Hierarchical Approach......Page 864
Basic Definitions......Page 865
Preference Modeling......Page 866
References and Further Reading......Page 867
Multidimensional Scaling......Page 868
Multidimensional Scaling: An Introduction......Page 871
Multilevel Analysis, Hierarchical Linear Models......Page 872
More Than Two Levels......Page 873
Inference......Page 874
Multinomial Distribution......Page 875
The Multi-Party Inference Reality......Page 877
Uncongeniality in Multiple Imputation Inference......Page 879
References and Further Reading......Page 880
Any Contrast Comparisons......Page 881
About the Authors......Page 882
A General Multiple Comparisons Problem......Page 883
Example......Page 884
Multiple Imputation and Combining Estimates......Page 885
Bootstrap EM......Page 886
Software......Page 887
Multiple Statistical Decision Theory......Page 888
Probability and Single Stage Sampling......Page 889
Cluster and Multistage Sampling......Page 890
References and Further Reading......Page 891
Function Selection Procedure (FSP)......Page 892
Multivariable Fractional Polynomial (MFP) Procedure......Page 893
About the Authors......Page 894
Multivariate Analysis of Variance (MANOVA)......Page 895
Multivariate Data Analysis: An Overview......Page 897
About the Author......Page 898
Multivariate Normal Distributions......Page 900
References and Further Reading......Page 902
Multivariate Outliers......Page 903
References and Further Reading......Page 904
Multivariate Rank Procedures : Perspectives and Prospectives......Page 905
Multivariate Reduced-Rank Regression......Page 906
Multivariate Statistical Analysis......Page 908
Cross References......Page 911
References and Further Reading......Page 912
Some Properties......Page 913
Student t Distributions......Page 915
Gamma Distributions......Page 916
Distributions of Latent Roots......Page 917
Binomial, Multinomial, and Related......Page 918
Other Distributions......Page 919
References and Further Reading......Page 920
Multivariate Statistical Process Control......Page 921
Multivariate Statistical Simulation......Page 923
Multivariate Techniques: Robustness......Page 925
References and Further Reading......Page 927
National Account Statistics......Page 929
Network Models in Probability and Statistics......Page 931
References and Further Reading......Page 932
Network Sampling......Page 933
Types of Neural Network......Page 934
Supervised Neural Networks......Page 935
Unsupervised Neural Networks......Page 936
Neyman-Pearson Lemma......Page 937
References and Further Reading......Page 938
Nonlinear Mixed Effects Models......Page 939
About the Author......Page 941
Introduction
......Page 942
On the Existence of the Least Square Estimators......Page 943
Optimality Criteria......Page 944
Nonlinear Regression......Page 945
Nonlinear Time Series Analysis......Page 947
About the Author......Page 949
Nonparametric Density Estimation......Page 950
Meanings of the Word ``Nonparametric''......Page 951
Wavelet Estimation......Page 952
References and Further Reading......Page 953
Nonparametric Estimation Based on Incomplete Observations......Page 954
Nonparametric Models for ANOVA and ANCOVA Designs......Page 956
References and Further Reading......Page 959
Overview......Page 960
About the Author......Page 961
Nonparametric Rank Tests......Page 962
Nonparametric Regression Based on Ranks......Page 964
The Statistical Model......Page 966
Nonparametric Statistical Inference......Page 969
About the Authors......Page 970
Non-probability Sampling Survey Methods......Page 971
Sampling from Mobile Human Populations within Small Areas......Page 972
References and Further Reading......Page 973
Nonresponse in Surveys......Page 974
References and Further Reading......Page 975
Nonresponse in Web Surveys......Page 976
References and Further Reading......Page 979
Coverage Errors......Page 980
Instrument Errors......Page 981
References and Further Reading......Page 982
Inversion......Page 983
Brief Historical Background......Page 987
Important Properties and Results......Page 988
Importance of Normal Distribution in Statistics......Page 989
References and Further Reading......Page 990
Normal Scores......Page 991
The Importance of Testing for Normality......Page 992
Types of Normality Tests......Page 993
About the Author......Page 994
References and Further Reading......Page 995
Null-Hypothesis Significance Testing: Misconceptons......Page 998
References and Further Reading......Page 1000
Newton–Cotes Quadrature......Page 1001
Determination of Weights in Gaussian Quadrature......Page 1002
Error in Monte Carlo Quadrature......Page 1003
Numerical Methods for Stochastic Differential Equations......Page 1004
References and Further Reading......Page 1005
Omnibus Test for Departures from Normality......Page 1006
About the Authors......Page 1007
Textbooks......Page 1009
Data Analysis......Page 1010
Introduction......Page 1011
Optimality Criteria......Page 1012
About the Author......Page 1013
Exact and Approximate Designs......Page 1014
Optimality Conditions and Algorithms......Page 1015
Optimal Shrinkage Estimation......Page 1016
Optimal Shrinkage Estimation Strategy......Page 1017
About the Author......Page 1018
Optimal Shrinkage Preliminary Test Estimation......Page 1019
Shrinkage Preliminary Test Estimation......Page 1020
Optimal Statistical Inference in Financial Engineering......Page 1021
Cross References......Page 1022
Optimal Stopping Rules......Page 1023
About the Author......Page 1024
Distortions of Hypothetical Models......Page 1025
Cross References......Page 1027
Criteria of Optimality......Page 1028
About the Author......Page 1029
Order Statistics......Page 1030
Ordered Statistical Data: Recent Developments......Page 1031
References and Further Reading......Page 1033
Outliers......Page 1034
Accommodation......Page 1035
References and Further Reading......Page 1036
Panel Data......Page 1037
Introduction......Page 1038
Nonparametric Approach to Reliability......Page 1039
Parametric Versus Nonparametric Tests......Page 1041
Introduction......Page 1042
Restricted Pareto Sampling......Page 1043
Introduction......Page 1044
Partial Least Squares Regression......Page 1045
Introduction......Page 1046
Design of a Pattern Classifier......Page 1047
Preliminaries......Page 1048
Discrete Distributions......Page 1049
Permutation Tests......Page 1050
Pharmaceutical Statistics: Bioequivalence......Page 1052
Philosophical Foundations of Statistics......Page 1053
References and Further Reading......Page 1054
Philosophy of Probability......Page 1055
References and Further Reading......Page 1058
Point Processes......Page 1059
About the Author......Page 1060
Poisson Distribution and Its Application in Statistics......Page 1061
References and Further Reading......Page 1062
Poisson Processes on the Real Line......Page 1063
Poisson Processes on Abstract Spaces......Page 1064
Introduction......Page 1065
About the Author......Page 1066
Population Projections......Page 1067
Mean-Variance Analysis and its Justification......Page 1068
About the Author......Page 1069
Posterior Consistency in Bayesian Nonparametrics......Page 1070
References and Further Reading......Page 1071
About the Author......Page 1072
Reasons for Applying Data Preprocessing......Page 1073
Data Integration......Page 1074
References and Further Reading......Page 1075
Presenting the Data or Summary Tables That will be Analyzed......Page 1076
A Few Suggestions to Statisticians Desiring to Increase the Validity of and Weight Given to Statistical and Scientific Evidence......Page 1081
Cross References......Page 1083
An Example......Page 1084
How Many Components?......Page 1085
References and Further Reading......Page 1086
A Prototypical Policy Evaluation Problem......Page 1087
An Index Model of Choice and Treatment Effects: Definitions and Unifying Principles......Page 1088
Definitions of Treatment Effects in the Two Outcome Model......Page 1090
The Weights for a Generalized Roy Model......Page 1092
The Basic Principles Underlying the Identification of the Leading Econometric Evaluation Estimators......Page 1095
Matching......Page 1104
References and Further Reading......Page 1107
Results and Examples......Page 1109
Probabilistic Network Models......Page 1110
Introduction......Page 1111
Infinite Divisibility......Page 1112
Sources of Uncertainty in Statistics......Page 1113
The Kolmogorov Axioms......Page 1114
References and Further Reading......Page 1115
Probability, History of......Page 1116
About the Author......Page 1117
Introduction......Page 1118
Probit Model......Page 1119
Cross References......Page 1120
Promoting, Fostering and Development of Statistics in Developing Countries......Page 1121
Properties of Estimators......Page 1122
Cross References......Page 1124
Proportions, Inferences, and Comparisons......Page 1125
Psychiatry, Statistics in......Page 1126
Cross References......Page 1127
Cross References......Page 1128
The Null Hypothesis Significance Testing Controversy......Page 1129
About the Author......Page 1131
Public Opinion Polls......Page 1132
About the Author......Page 1133
P–Values......Page 1134
P-Values, Combining of......Page 1135
Pyramid Schemes......Page 1137
References and Further Reading......Page 1139
The Basic Set-Up: Risk Measures......Page 1140
Statistical Estimation......Page 1141
References and Further Reading......Page 1142
Questionnaire......Page 1143
Queueing Theory......Page 1145
References and Further Reading......Page 1147
R Language......Page 1148
2. Martingales.......Page 1150
7. The Radon–Nikodým derivative between two Markov jump processes.......Page 1151
References and Further Reading......Page 1152
Random Coefficient Models......Page 1153
Random Field......Page 1154
Basic Concepts......Page 1157
Limiting Properties of Eigenvectors......Page 1158
Set Partitions......Page 1159
Partition Processes and Partition Structures......Page 1160
Exchangeable Random Permutations......Page 1161
On the Number of Unseen Species......Page 1162
Equivariant Partition Models......Page 1163
Cluster Processes and Classification Models......Page 1164
References and Further Reading......Page 1165
Formal Definition......Page 1166
Random Walk......Page 1167
Randomization......Page 1169
Randomization Tests......Page 1171
References and Further Reading......Page 1172
RT-2......Page 1173
Introduction......Page 1174
Balanced Ranked Set Samples......Page 1175
References and Further Reading......Page 1176
Basic Formulations of the Ranking and Selection Problem......Page 1177
References and Further Reading......Page 1179
Augmented Ranking......Page 1180
Rao–Blackwell Theorem......Page 1181
References and Further Reading......Page 1182
Rating Scales......Page 1183
Definitions of Records......Page 1184
Sequential Ranks and Record Indicators......Page 1185
Distributions of Record Values......Page 1187
Cross References......Page 1189
References and Further Reading......Page 1190
Structure of a RP model......Page 1191
Learning the RP Model......Page 1192
Strengths and Weaknesses of RP Models......Page 1193
About the Author......Page 1194
Regression Diagnostics......Page 1195
About the Authors......Page 1196
Linear Regression Models......Page 1197
Estimation of Covariance Matrix......Page 1198
About the Author......Page 1199
Symmetrical Nonlinear Models......Page 1200
Introduction......Page 1201
References and Further Reading......Page 1202
Transformations......Page 1203
Internal Properties......Page 1204
Renewal Processes......Page 1206
References and Further Reading......Page 1209
References and Further Reading......Page 1210
Representative Samples......Page 1211
References and Further Reading......Page 1212
Factorial and Block Designs......Page 1213
Common Experimental Designs......Page 1214
Common Quasi-Experimental Designs......Page 1215
Residuals......Page 1216
About the Author......Page 1217
Response Surface Methodology......Page 1218
References and Further Reading......Page 1220
Ridge and Surrogate Ridge Regressions......Page 1221
Cross References......Page 1222
Education......Page 1223
Journals......Page 1224
Cross References......Page 1225
Likelihood......Page 1226
Recovery......Page 1227
References and Further Reading......Page 1228
Robust Inference......Page 1229
References and Further Reading......Page 1230
Diagnostic Measures......Page 1231
Cross References......Page 1232
Outliers......Page 1233
L Estimates......Page 1235
General Considerations......Page 1236
Introduction......Page 1237
The Breakdown Point......Page 1238
Heuristic Aspects of Robustness......Page 1239
ROC Curves......Page 1240
The Importance of Statistics......Page 1243
Statistics and Uncertainty......Page 1245
References and Further Reading......Page 1246
Statistics' Role in Quantitative Education......Page 1247
Fundamental Understanding of the Scientific Method......Page 1248
Development/Enhancement of the Ability to Use the Higher-Order Analytic and Critical Thinking Skills Needed to Understand and C......Page 1249
References and Further Reading......Page 1250
Some Issues and Challenges Facing Developing Countries......Page 1251
Rubin Causal Model......Page 1252
About the Author......Page 1253
References and Further Reading......Page 1254
The Saddlepoint Approximation......Page 1255
Sample Size to Achieve a Given Variance or Relative Variance......Page 1257
Software for Sample Size Determination......Page 1258
Sample Survey Methods......Page 1259
Cross References......Page 1260
Sampling Algorithms......Page 1261
What is it?......Page 1262
Monte Carlo Simulations......Page 1264
Introduction......Page 1265
Systematic Sampling......Page 1266
Cluster and Multistage Sampling......Page 1267
About the Authors......Page 1268
Sampling Problems for Stochastic Processes......Page 1269
References and Further Reading......Page 1270
Scales of Measurement......Page 1271
Scales of Measurement and Distributional Assumptions......Page 1273
Rank Transformations and Appropriate Statistics......Page 1274
References and Further Reading......Page 1276
Seasonal Integration......Page 1277
Seasonal Cointegration......Page 1278
References and Further Reading......Page 1279
Seasonal Modeling......Page 1280
An Example......Page 1281
Selection of Appropriate Statistical Methods in Developing Countries......Page 1282
Cross References......Page 1283
References and Further Reading......Page 1284
Cross References......Page 1285
Use of Sensitivity Analysis......Page 1286
Design and Estimators......Page 1287
Variance-Based Sensitivity Measures......Page 1288
References and Further Reading......Page 1289
Sensometrics: Statistics, Psychometrics, or Chemometrics?......Page 1290
Example 2: Sensory Difference and Similarity Test Data......Page 1291
References and Further Reading......Page 1292
Introduction: Sequential Testing and Sequential Probability Ratios......Page 1293
Finite Termination and Average Sample Number (ASN)......Page 1294
About the Authors......Page 1295
Sequential Ranks......Page 1296
Cross References......Page 1298
Why Sequential Sampling?......Page 1299
Purely Sequential Sampling......Page 1300
Which Areas Are Hot Beds for Sequential Sampling?......Page 1301
Sex Ratio in National Birth Registers......Page 1302
References and Further Reading......Page 1303
Sign Test......Page 1304
References and Further Reading......Page 1305
The p-Value......Page 1306
Inversion of a Family of Tests to Obtain Confidence Regions......Page 1307
Cross References......Page 1308
Significance Tests, History and Logic of......Page 1309
References and Further Reading......Page 1310
The innumerable misuses of significance tests......Page 1311
Concluding Remarks......Page 1312
Simes' Test in Multiple Testing......Page 1313
References and Further Reading......Page 1314
Simple Linear Regression......Page 1315
Simple Random Sample......Page 1316
Cross References......Page 1317
Simpson's Paradox......Page 1318
Simulation Based Bayes Procedures for Model Structures with Non-Elliptical Posteriors......Page 1320
References and Further Reading......Page 1322
Extensions of the Basic SSA......Page 1323
References and Further Reading......Page 1324
SIPOC and COPIS: Business Flow – Business Optimization Connection in a Six Sigma Context......Page 1325
References and Further Reading......Page 1326
The DMAIC Model......Page 1327
Skewness......Page 1328
Skew-Normal Distribution......Page 1330
Skew-Symmetric Families of Distributions......Page 1332
Introduction......Page 1334
Design-Based Methods......Page 1335
Unit Level Random Effects Model for Binary Data......Page 1336
Univariate Smoothing Splines......Page 1337
Splines on Riemannian Manifolds......Page 1338
References and Further Reading......Page 1340
Density Estimation......Page 1341
Additive Models......Page 1342
References and Further Reading......Page 1343
Exponential Random Graph Models......Page 1344
Longitudinal Models......Page 1345
Social Statistics......Page 1346
Introduction......Page 1347
Contingency Table Analysis......Page 1348
Introduction......Page 1349
About the Author......Page 1350
Geostatistics......Page 1351
Point Process Analysis and Random Sets......Page 1353
Lattice Data Analysis......Page 1354
References and Further Reading......Page 1355
Introduction......Page 1356
An Application......Page 1357
References and Further Reading......Page 1358
Sport, Statistics in......Page 1359
About the Authors......Page 1360
Spreadsheets in Statistics......Page 1361
Spurious Correlation......Page 1362
About the Author......Page 1364
St. Petersburg Paradox......Page 1365
Definition......Page 1366
References and Further Reading......Page 1367
Drug Release from Pharmaceutical Systems......Page 1368
Defining the Statistical Problem......Page 1369
Introduction......Page 1371
Generalized Estimating Equations Models......Page 1372
About the Author......Page 1373
Statistical Approaches to Protecting Confidentiality in Public Use Data......Page 1374
References and Further Reading......Page 1375
References and Further Reading......Page 1377
Desirable Qualities for a Statistical Consultant......Page 1378
Cross References......Page 1379
Optimal Designs......Page 1380
Factorial Designs......Page 1381
Fractional Factorial Designs of the Type 2k-p......Page 1382
References and Further Reading......Page 1383
Discrete Distributions......Page 1384
Continuous Distributions......Page 1385
Moments and Other Measures......Page 1386
Cross References......Page 1388
Distance Sampling......Page 1389
Future......Page 1390
References and Further Reading......Page 1391
Empirical Estimation of......Page 1392
Cross References......Page 1393
Statistical Evidence......Page 1394
Cross References......Page 1396
Statistical Fallacies......Page 1397
References and Further Reading......Page 1399
Statistical Fallacies: Misconceptions, and Myths......Page 1400
References and Further Reading......Page 1404
Statistical Genetics......Page 1405
Statistical Inference......Page 1406
Statistical Inference for Quantum Systems......Page 1408
Cross References......Page 1410
Markov Chains and Sequences......Page 1411
Bienayme-Galton-Watson Branching Process......Page 1412
Non-parametric Modeling Based on Functional Estimation......Page 1413
Counting and Pure Jump Markov Processes......Page 1414
Diffusion Processes......Page 1415
Efficiency of Estimators......Page 1416
References and Further Reading......Page 1417
Statistical Inference in Ecology......Page 1418
References and Further Reading......Page 1420
Frequentist Statistical Inference......Page 1421
Different Forms of Statistical Inference......Page 1422
Bayesian Inference......Page 1425
References and Further Reading......Page 1426
Statistical Literacy, Reasoning, and Thinking......Page 1427
Words That Characterize Assessment Items for Statistical Literacy, Reasoning, and Thinking......Page 1428
References and Further Reading......Page 1429
Characterizing Functions of Non-Precise Data......Page 1430
About the Author......Page 1431
Cohort Studies......Page 1432
Regression vs. Non-Regression Methods......Page 1434
Overview......Page 1435
Black–Scholes Model......Page 1436
Conclusions......Page 1437
Statistical Modelling in Market Research......Page 1438
Statistical Natural Language Processing......Page 1440
Problem Description......Page 1441
Applicant Recognition for Project Realization with Good Contract Risk......Page 1442
Signal Detection in Clutter......Page 1443
References and Further Reading......Page 1445
Statistical Publications, History of......Page 1446
Quality: A Brief Introduction......Page 1447
Usual Statistical Techniques in SQC......Page 1448
References and Further Reading......Page 1450
Univariate Control Charts Versus Multivariate Control Charts......Page 1451
SPC Applications in Service Industries......Page 1452
References and Further Reading......Page 1453
Statistical Signal Processing......Page 1454
Array Model......Page 1455
Statistical Significance......Page 1456
Cross References......Page 1457
BMDP, SAS, SPSS......Page 1458
S, LISP-STAT, R......Page 1459
About the Author......Page 1460
Statistical View of Information Theory......Page 1461
Acknowledgment......Page 1462
What Is Needed?......Page 1463
Some Working Initiatives......Page 1464
Introduction......Page 1465
Bold Play in Red and Black......Page 1466
Statistics and the Law......Page 1467
References and Further Reading......Page 1469
University Education in Statistics......Page 1470
Statistics in the Workplace......Page 1471
Introduction......Page 1472
Threshold Exceedances......Page 1473
Further Reading......Page 1474
Introduction......Page 1475
Distance between Ranked Lists......Page 1476
Aggregation of Ranked Lists......Page 1477
Cross Reference......Page 1478
Statistics, Targeted Clinical Trials,and Stratified Medicine......Page 1479
Cross References......Page 1480
Staatswissenschaft and Political Arithmetic......Page 1481
Statistics and the Statistical Method: The Theory of Errors......Page 1482
Jakob Bernoulli, De Moivre, Bayes: Chance and Design......Page 1483
The Theory of Probability and Statistics: Quetelet......Page 1485
New Times: Great Progress and the Soviet cul-de-sac......Page 1486
The Two Streams of Statistical Thought......Page 1488
References and Further Reading......Page 1489
Statistics: An Overview......Page 1492
References and Further Reading......Page 1496
Example 3: Placeboes in Surgery......Page 1497
Statistical Science is a Wonderful Subject......Page 1498
The Experimental Cycle......Page 1499
Cross References......Page 1500
Stem-and-Leaf Plot......Page 1501
Introduction......Page 1502
The Cumulative Exposure Model......Page 1503
Cross References......Page 1504
Stochastic Difference Equations and Applications......Page 1505
References and Further Reading......Page 1507
Stochastic Differential Equations......Page 1508
Stochastic Global Optimization......Page 1509
References and Further Reading......Page 1511
Modeling by Stochastic Differential Equations......Page 1512
References and Further Reading......Page 1513
Stochastic Modeling Analysis and Applications......Page 1514
Random Walk Modeling Approach (Ladde and Ladde ch571:ladde2009)......Page 1515
Sequential Colored Noise Modeling Approach (Ladde and Ladde ch571:ladde2009; Wong ch571:wong1971)......Page 1517
Cross References......Page 1518
Stochastic Models of Transport Processes......Page 1519
References and Further Reading......Page 1521
Definition of a Stochastic Process......Page 1522
Construction of Canonical Processes......Page 1523
Series Expansion in L2......Page 1524
Extensions of the Theory......Page 1525
Cross References......Page 1526
Martingales in Finance......Page 1527
Insurance Risk Model......Page 1528
Definitions......Page 1529
State and Time Discretized Process......Page 1530
Markov Chains......Page 1531
Birth and Death Process......Page 1532
Martingale Process......Page 1533
About the Author......Page 1534
Estimation Under Simple Random Sampling Within Strata......Page 1535
Variance Estimation for Stratified Samples......Page 1536
Controlled Selection......Page 1537
Strong Approximations in Probability and Statistics......Page 1538
Mathematical Representation......Page 1540
Model Estimation......Page 1541
Equivalent Structural Equation Models......Page 1542
Introduction......Page 1543
State Space Form......Page 1544
References and Further Reading......Page 1545
Student's t-Distribution......Page 1546
Introduction......Page 1547
One-Sample t-Test......Page 1548
Two Independent Samples......Page 1549
References and Further Reading......Page 1550
Histogram as Density Estimator......Page 1551
The Rules in Practice......Page 1552
About the Author......Page 1553
One-Parameter Case......Page 1554
Multi-Parameter Case......Page 1555
Cross References......Page 1556
Neyman Factorization......Page 1557
A Complete Sufficient Statistic......Page 1558
References and Further Reading......Page 1559
Varied Versions of the Basic Boxplot......Page 1560
Outlier Rule......Page 1561
References and Further Reading......Page 1562
Superpopulation Models in Survey Sampling......Page 1563
References and Further Reading......Page 1564
Overviews......Page 1565
Complex Situations......Page 1566
References and Further Reading......Page 1567
Statistical Analysis......Page 1568
About the Author......Page 1569
References and Further Reading......Page 1570
von Mises Expansions of Target Functionals......Page 1571
Final Remarks......Page 1572
Telephone Sampling: Frames and Selection Techniques......Page 1573
References and Further Reading......Page 1574
Asymptotically Linear Statistics......Page 1575
Distribution Free Versions of Empirical Processes......Page 1576
Cross References......Page 1577
Introduction......Page 1578
Similar and Location-Invariant Tests......Page 1579
Introduction......Page 1580
Alternative Approaches......Page 1581
References and Further Reading......Page 1582
Tests for Equality of Variances of k Populations......Page 1583
References and Further Reading......Page 1584
The Probability Integral Transformation......Page 1585
Testing for Interdependence......Page 1586
About the Author......Page 1588
Time Series......Page 1589
Acknowledgments......Page 1592
Time Series Models to Determine the Death Rate of a Given Disease......Page 1593
About the Author......Page 1594
Regression with Autocorrelated Errors......Page 1595
Regression with Heteroscedasticity......Page 1596
References and Further Reading......Page 1597
Total Survey Error......Page 1598
Tourism Statistics......Page 1600
Two-Stage Least Squares......Page 1604
Trend Estimation......Page 1601
References and Further Reading......Page 1606
Unbiased Estimators and Their Applications......Page 1607
Properties of the Uniform Distribution......Page 1609
Uniform Distribution and Modelingof Random Variables......Page 1610
Uniform Experimental Design......Page 1611
References and Further Reading......Page 1612
Algorithmic Generators......Page 1613
Multivariate Uniformity......Page 1614
Linear recurrences modulo m......Page 1615
Recommendations......Page 1616
References and Further Reading......Page 1617
Historical Perspective......Page 1618
Properties......Page 1620
References and Further Reading......Page 1621
U-Statistics......Page 1622
References and Further Reading......Page 1623
Validity of Scales......Page 1624
References and Further Reading......Page 1625
Cross References......Page 1626
Variance......Page 1627
Nominal Case......Page 1629
Ordinal Case......Page 1630
About the Author......Page 1631
The Model Setup......Page 1632
Extensions......Page 1633
References and Further Reading......Page 1634
Some Typical Roles of Weak Convergence in Probability......Page 1635
Relative Compactness, Tightness and Prohorov's Theorem......Page 1636
Weibull Distribution......Page 1637
Introduction......Page 1639
A New Way of Developing Weighted Correlation Coefficients......Page 1640
Weighted U-Statistics......Page 1641
Wilcoxon–Mann–Whitney Test......Page 1642
References and Further Reading......Page 1643
Wilcoxon-Signed-Rank Test......Page 1644
References and Further Reading......Page 1645
List of Entries......Page 1646