Advances on Methodological and Applied Aspects of Probability and Statistics

Advances on Methodological and Applied Aspects of Probability and Statistics......Page 4
CONTENTS......Page 6
PREFACE......Page 22
LIST OF CONTRIBUTORS......Page 24
LIST OF TABLES......Page 30
LIST OF FIGURES......Page 36
Part I: Applied Probability......Page 41
1.1 INTRODUCTION......Page 43
1.2 MORAN’S MODEL FOR THE FINITE DAM......Page 44
1.3 A CONTINUOUS TIME MODEL FOR THE DAM......Page 46
Remarks......Page 47
1.4 A MODEL FOR DATA COMMUNICATION SYSTEMS......Page 48
REFERENCES......Page 51
2.1 INTRODUCTION......Page 53
2.2 M.L.E. IN MARKOVIAN SYSTEMS......Page 55
2.3 M.L.E. IN NON-MARKOVIAN SYSTEMS......Page 56
2.4 M.L.E. FOR SINGLE SERVER QUEUES USING WAITING TIME DATA......Page 58
2.5 M.L.E. USING SYSTEM TIME......Page 59
2.6 M.L.E. IN M/G/1 USING QUEUE LENGTH DATA......Page 61
2.7 M.L.E. IN GI/M/1 USING QUEUE LENGTH DATA......Page 64
2.8 SOME OBSERVATIONS......Page 66
REFERENCES......Page 67
CHAPTER 3: NUMERICAL EVALUATION OF STATE PROBABILITIES AT DIFFERENT EPOCHS IN MULTISERVER GI/Geom/m QUEUE......Page 70
3.1 INTRODUCTION......Page 72
3.2 MODEL AND SOLUTION: GI/Geom/m (EAS)......Page 73
3.2.1 Evaluation of…......Page 77
3.3 GI/Geom/m (LAS-DA)......Page 79
3.3.2 Outside observer’s distribution......Page 82
3.4 NUMERICAL RESULTS......Page 83
REFERENCES......Page 86
4.1 INTRODUCTION......Page 87
4.2 THE GIb/M/1/N MODEL......Page 89
4.3 LATTICE PATH APPROACH......Page 90
4.4.1 Transient Probabilities......Page 91
4.4.2 Counting of Lattice Paths......Page 92
4.4.3 Notations......Page 93
4.5 BUSY PERIOD PROBABILITY FOR THE DISCRETIZED…MODEL......Page 100
4.6 CONTINUOUS…MODEL......Page 103
(i) … model......Page 104
4.8 NUMERICAL COMPUTATIONS AND COMMENTS......Page 105
REFERENCES......Page 107
Part II: Models and Applications......Page 125
5.1 INTRODUCTION......Page 127
5.2 CURRENT MEASURES FOR DISTRIBUTIONAL MORPHOLOGY......Page 128
5.3 (ξ1, ξ2) SYSTEM......Page 131
5.4 ASYMPTOTIC DISTRIBUTIONS OF J1, J2......Page 133
5.5 MISCELLANEOUS REMARKS......Page 135
REFERENCES......Page 137
6.1 INTRODUCTION......Page 141
6.2 INTERPRETATION OF BVG MODEL ASSUMPTIONS......Page 142
6.3 THE MODEL UNDER THE ENVIRONMENTAL EFFECT......Page 144
6.4 DATA ANALYSIS WITH BVG MODEL......Page 145
REFERENCES......Page 149
Part III: Estimation and Testing......Page 151
7.1 INTRODUCTION......Page 153
7.2.1 Area Level Models......Page 155
7.2.2 Unit Level Models......Page 158
7.3 MODEL-BASED INFERENCE......Page 160
7.3.1 EBLUP Method......Page 161
7.3.2 EB Method......Page 164
7.3.3 HB Method......Page 165
Basic models......Page 168
Multivariate models......Page 169
Disease mapping models......Page 170
Multivariate nested error regression models......Page 171
Logistic linear mixed models......Page 172
REFERENCES......Page 173
8.1 INTRODUCTION......Page 181
8.2 EXISTING LITERATURE......Page 183
8.3 MIXTURE OF TWO VON-MISES DISTRIBUTIONS......Page 184
8.4 PRIOR SPECIFICATION......Page 186
8.5 PRIOR AND POSTERIOR PROBABILITY OF UNIMODALITY......Page 187
8.6 THE BAYES FACTOR......Page 188
8.7 APPLICATION......Page 189
8.8 SOME ISSUES......Page 191
REFERENCES......Page 193
9.1 INTRODUCTION......Page 199
9.2 EXAMINING THE LIKELIHOOD FUNCTION......Page 201
9.3 ALGORITHM TO FIND MLE’S......Page 203
9.4 NUMERICAL EXAMPLE......Page 205
REFERENCES......Page 206
10.1 INTRODUCTION......Page 209
10.2.1 Ranked Set Sampling......Page 211
10.2.2 Modified Ranked Set Sampling......Page 212
10.2.3 New Ranked Set Sampling......Page 213
10.3 LAPLACE DISTRIBUTION......Page 214
10.4.1 Joint Estimation of mu and sigma......Page 216
10.4.3 Estimation of sigma......Page 217
REFERENCES......Page 218
11.1 INTRODUCTION......Page 223
11.2 THE MONOTONICITY OF di’s......Page 225
11.3 RESULTS ON ORDERED COMPONENTS OF A RANDOM VECTOR......Page 227
REFERENCES......Page 231
Part IV: Robust Inference......Page 235
12.1 INTRODUCTION......Page 237
12.1.1 A Unifying Structure......Page 238
L-Statistics as statistical functionals......Page 240
GL-statistics as statistical functionals......Page 241
Two examples: Spread measures of Bickel and Lehmann......Page 242
12.3.1 Differentiation Methodology......Page 243
12.3.2 The Estimation Error in the U-Empirical Process......Page 244
12.3.3 Extended Glivenko-Cantelli Theory......Page 245
12.3.4 Oscillation Theory, Generalized Order Statistics, and Bahadur Representations......Page 246
12.3.5 Estimation of the Variance of a U-Statistic......Page 247
12.4.1 Asymptotic Normality and the LIL......Page 248
12.4.3 Large Deviation Theory......Page 249
Location estimation......Page 250
Regression slope estimation......Page 251
Scale......Page 252
12.5.5 Robust Estimation of Exponential Scale Parameter......Page 253
REFERENCES......Page 254
CHAPTER 13: A CLASS OF ROBUST STEPWISE TESTS FOR MANOVA......Page 259
13.1 INTRODUCTION......Page 260
13.2.1 Robust Univariate Tests......Page 262
13.2.2 Combining Independent P-Values......Page 264
13.2.3 Modified Step Down Procedure......Page 265
13.3 ROBUST STEPWISE TESTS......Page 267
13.4.1 The Study......Page 268
REFERENCES......Page 271
14.1 INTRODUCTION......Page 281
14.2.1 General Mixed Linear Model......Page 283
14.2.2 Maximum Likelihood and Restricted Maximum Likelihood Estimators......Page 284
14.2.3 Robust Versions of ML and REML Estimators......Page 285
14.3 DESCRIPTION OF THE SIMULATION EXPERIMENT......Page 286
14.4.3 MSE’s of Estimators of…......Page 288
REFERENCES......Page 289
Part V\rRegression and Design......Page 301
CHAPTER 15: PERFORMANCE OF THE PTE BASED ON THE CONFLICTING W, LR AND LM TESTS IN REGRESSION MODEL......Page 302
15.1 INTRODUCTION......Page 303
15.2 THE TESTS AND PROPOSED ESTIMATORS......Page 304
15.3 BIAS, M AND RISK OF THE ESTIMATORS......Page 306
15.4.1 Bias Analysis of the Estimators......Page 308
15.4.2 M Analysis of the Estimators......Page 309
15.4.3 Risk Analysis of the Estimators......Page 310
15.5 EFFICIENCY ANALYSIS AND RECOMMENDATIONS......Page 312
15.6 CONCLUSION......Page 314
REFERENCES......Page 315
CHAPTER 16: ESTIMATION OF REGRESSION AND DISPERSION PARAMETERS IN THE ANALYSIS OF PROPORTIONS......Page 323
16.1 INTRODUCTION......Page 324
16.2.1 The Extended Beta-Binomial Likelihood......Page 325
16.2.2 The Quasi-Likelihood Method......Page 326
16.2.3 Estimation Using Quadratic Estimating Equations......Page 327
16.3 ASYMPTOTIC RELATIVE EFFICIENCY......Page 329
16.4 EXAMPLES......Page 332
16.5 DISCUSSION......Page 333
REFERENCES......Page 334
CHAPTER 17: SEMIPARAMETRIC LOCATION-SCALE REGRESSION MODELS FOR SURVIVAL DATA......Page 345
17.1 INTRODUCTION......Page 346
17.2 LIKELIHOOD FUNCTION FOR THE PARAMETRIC LOCATION-SCALE MODELS......Page 347
17.3.1 Application of Generalized Profile Likelihood to Semiparametric Location-Scale Regression Models......Page 348
17.3.2 Estimation and Large Sample Properties......Page 349
17.4 EXAMPLES OF SEMIPARAMETRIC LOCATION-SCALE REGRESSION MODELS......Page 350
17.5 AN EXAMPLE WITH CENSORED SURVIVAL DATA: PRIMARY BILIARY CIRRHOSIS (PBC) DATA......Page 352
REFERENCES......Page 353
APPENDIX: COMPUTATION OF THE ESTIMATES......Page 354
18.1 INTRODUCTION......Page 365
18.2.1 Orthogonality and Saturation......Page 367
Individual and familywise control of error rates......Page 369
Strong control of error rates......Page 370
18.3.1 Background......Page 371
Closed, step-down tests......Page 373
Iterative methods and sharper critical values: an open problem......Page 375
Directional inference: an open problem......Page 376
18.3.3 Individual Tests......Page 377
18.3.5 Simultaneous Confidence Intervals......Page 378
18.3.6 Adaptive Methods......Page 379
18.4 NON-ORTHOGONAL SATURATED DESIGNS......Page 380
18.4.1 Individual Confidence Intervals......Page 381
18.5 SUPER-SATURATED DESIGNS......Page 382
REFERENCES......Page 383
CHAPTER 19: ON ESTIMATING SUBJECT-TREATMENT INTERACTION......Page 389
19.1 INTRODUCTION......Page 390
19.2 AN ESTIMATOR OF S2D USING CONCOMITANT INFORMATION......Page 392
A general prediction approach......Page 394
19.3 AN ILLUSTRATIVE EXAMPLE......Page 399
19.4 SUMMARY/CONCLUSIONS......Page 400
REFERENCES......Page 401
Part VI: Sample Size and Methodology......Page 405
20.1 ESTABLISHING THERAPEUTIC EQUIVALENCE IN PARALLEL STUDIES......Page 407
20.1.1 Tests under Delta-Formulation (20.1.2)......Page 409
20.1.2 Tests under Relative Risk Formulation (ψ Formulation)......Page 411
Logarithmic transformation......Page 412
20.1.3 Confidence Bound Method for Delta Formulation......Page 413
20.2 SAMPLE SIZE FOR PAIRED DATA STUDIES......Page 414
20.2.1 Testing for Equality of Correlated Proportions......Page 415
Score test......Page 417
Test based on sample proportions......Page 418
A Wald type test......Page 419
REFERENCES......Page 420
21.1 INTRODUCTION......Page 423
21.2 FORMULATION OF THE PROBLEM......Page 425
21.3 THE MAIN RESULTS......Page 426
21.4 FIXED-WIDTH CONFIDENCE INTERVAL ESTIMATION......Page 435
REFERENCES......Page 438
Part VII: Applications to Industry......Page 439
22.1 INTRODUCTION......Page 441
Commitment of management......Page 442
Systems thinking......Page 443
Training considerations......Page 444
Graduate programme......Page 445
22.7 UNIVERSITY OF WATERLOO AND INDUSTRY......Page 446
Co-op students......Page 448
22.8 CONCLUDING REMARKS......Page 449
REFERENCES......Page 450
23.1 INTRODUCTION......Page 453
23.2 DESIGNS FOR CONTROL BASED ON H.P.D. SETS......Page 455
23.3 AN EXAMPLE OF THE USE OF HPD DESIGNS......Page 457
23.4 DESIGNS FOR R.S.B. BASED ON C.P. INTERVALS......Page 458
23.5 CONCLUDING REMARKS......Page 460
APPENDIX: MODEL USED IN SECTION 23.3......Page 461
REFERENCES......Page 462
24.1 INTRODUCTION......Page 465
24.2 THE CLASS......Page 466
24.3.1 Coherent Structures......Page 469
24.3.2 Convolutions......Page 471
24.3.3 Mixtures......Page 473
24.4 THE DISCRETE CLASS…AND ITS DUAL......Page 474
24.5 …AGING WITH SHOCKS......Page 476
REFERENCES......Page 480
25.1 INTRODUCTION......Page 481
25.2.1 Model......Page 483
25.2.2 Modification of Greenberg and Stokes Estimators......Page 484
25.2.3 An Empirical Bayes Estimator......Page 486
25.2.4 Comparison of Estimators......Page 488
25.2.5 Example......Page 490
25.3.1 Estimators......Page 492
25.4 SUGGESTIONS FOR FURTHER RESEARCH......Page 494
Appendix A1.2: Calculations of Probabilities......Page 495
Appendix A2.1: Bias and the MSE Derivation for Ûnew,2abknown......Page 496
Appendix A2.2: MSE of estimators, ÛGS,1, ÛGS,2 or Ûnew,1......Page 498
REFERENCES......Page 499
26.1 THE GE ENVIRONMENT......Page 505
26.2 SIX SIGMA......Page 507
26.3.1 Introduction......Page 508
26.3.3 Reliability Issue with a Supplied Part......Page 509
26.3.4 Constructing a Reliability Database......Page 510
26.4 SOME SURPRISES COMING TO INDUSTRY......Page 511
Recommendations to Students......Page 512
Recommendations to Departments......Page 513
REFERENCES......Page 514
Part VIII: Applications to Ecology, Biology and Health......Page 515
27.1 CERTAIN CHALLENGES AND ADVANCES IN TRANSECT SAMPLING......Page 517
27.1.1 Deep-Sea Red Crab......Page 518
27.1.2 Bivariate Sighting Functions......Page 520
The method......Page 522
27.2.1 Estimating Prevalence Using Composites......Page 526
Asymptotic performance of compositing......Page 527
Optimal composite sample size and its robustness......Page 528
Bias reduction......Page 530
27.2.2 Two-Way Compositing......Page 531
27.2.3 Compositing and Stochastic Monotonicity......Page 532
Pareto distribution......Page 533
27.3.1 Adaptive Sampling and GIS......Page 535
27.3.2 Using Covariate-Species Community Dissimilarity to Guide Sampling......Page 539
REFERENCES......Page 543
28.1 INTRODUCTION......Page 547
28.2 PHYSIOLOGICAL BACKGROUND......Page 548
28.3.1 Moment Methods......Page 550
28.3.2 Intensity Function Based Methods......Page 552
28.3.3 Frequency Domain Methods......Page 553
28.3.4 Graphical Methods......Page 556
28.3.5 Parametric Methods......Page 558
REFERENCES......Page 561
CHAPTER 29: SOME STATISTICAL ISSUES INVOLVING MULTIGENERATION CYTONUCLEAR DATA......Page 565
29.1 INTRODUCTION......Page 566
29.2 NEUTRALITY OR SELECTION?......Page 567
29.2.1 Sampling Schemes for Multi-Generation Data......Page 569
29.2.2 An Omnibus Test......Page 570
29.2.3 Application to Gambusia Data......Page 571
29.2.5 Tests Against a Specific Selection Model......Page 572
Examples of selection schemes......Page 573
Construction of a test statistic......Page 574
Calculation of P-value using bootstrap......Page 576
Power and sample size......Page 577
29.3 INFERENCE FOR THE SELECTION COEFFICIENTS......Page 578
29.3.2 An Approximate Likelihood......Page 579
REFERENCES......Page 581
30.1 INTRODUCTION......Page 587
30.2 CONFIDENCE INTERVALS FOR CER......Page 588
Symmetric interval......Page 589
30.3 COMPARISON OF INTERVALS......Page 590
Specifying distributions and parameters......Page 592
30.5 RESULTS......Page 593
30.6 RECOMMENDATIONS......Page 598
REFERENCES......Page 599
31.1 INTRODUCTION......Page 601
31.2.1 Flowgraph Models for Series Systems......Page 603
31.2.2 Flowgraph Models for Parallel Systems......Page 604
31.2.3 Flowgraph Models with Feedback......Page 605
31.3 RELIABILITY APPLICATION: HYDRAULIC PUMP SYSTEM......Page 606
31.4 SURVIVAL ANALYSIS APPLICATION: A FEED FORWARD MODEL FOR HIV......Page 608
31.5 CONCLUSION......Page 610
REFERENCES......Page 611
Part IX: Applications to Economics and Management......Page 613
32.1 INTRODUCTION......Page 615
32.2.1 The Elements of the IM Test for the Output Model......Page 617
32.2.2 The Elements of the IM Test for the Cost Model......Page 622
32.3.1 Output Model Estimation......Page 624
32.3.2 Moments Test for the Output Model......Page 625
32.3.4 Moments Test for the Cost Model......Page 627
32.4 CONCLUSION......Page 629
APPENDIX A: Derivations of the elements of IM test for the output model......Page 630
APPENDIX B: Derivations of the elements of the IM test for the cost model......Page 632
REFERENCES......Page 635
33.1 THE INTRODUCTION AND MOTIVATION......Page 637
33.2 GLM, GEE & PANEL LOGIT/PROBIT (LDV) MODELS......Page 641
33.2.1 GLM for Panel Data......Page 645
33.2.2 Random Effects Model from Econometrics......Page 646
33.2.3 Derivation of GEE, the Estimator for beta and Standard Errors......Page 647
33.3 GEE ESTIMATION OF CEO TURNOVER AND THREE HYPOTHESES......Page 649
Managerial characteristics......Page 651
Regional variables......Page 652
Customer wealth......Page 653
Turnover and allowed returns......Page 654
Managerial turnover and electricity price changes......Page 655
33.4 CONCLUDING REMARKS......Page 656
REFERENCES......Page 657