Advances on Methodological and Applied Aspects of Probability and Statistics

Advances on Methodological and Applied Aspects of Probability and Statistics......Page 3
CONTENTS......Page 5
PREFACE......Page 21
LIST OF CONTRIBUTORS......Page 23
LIST OF TABLES......Page 28
LIST OF FIGURES......Page 34
Part I: Applied Probability......Page 39
1.1 INTRODUCTION......Page 40
1.2 MORAN’S MODEL FOR THE FINITE DAM......Page 41
1.3 A CONTINUOUS TIME MODEL FOR THE DAM......Page 43
Remarks......Page 44
1.4 A MODEL FOR DATA COMMUNICATION SYSTEMS......Page 45
REFERENCES......Page 48
2.1 INTRODUCTION......Page 49
2.2 M.L.E. IN MARKOVIAN SYSTEMS......Page 51
2.3 M.L.E. IN NON-MARKOVIAN SYSTEMS......Page 52
2.4 M.L.E. FOR SINGLE SERVER QUEUES USING WAITING TIME DATA......Page 54
2.5 M.L.E. USING SYSTEM TIME......Page 55
2.6 M.L.E. IN M/G/1 USING QUEUE LENGTH DATA......Page 57
2.7 M.L.E. IN GI/M/1 USING QUEUE LENGTH DATA......Page 60
2.8 SOME OBSERVATIONS......Page 62
REFERENCES......Page 63
CHAPTER 3: NUMERICAL EVALUATION OF STATE PROBABILITIES AT DIFFERENT EPOCHS IN MULTISERVER GI/Geom/m QUEUE......Page 66
3.1 INTRODUCTION......Page 67
3.2 MODEL AND SOLUTION: GI/Geom/m (EAS)......Page 68
3.2.1 Evaluation of…......Page 72
3.3 GI/Geom/m (LAS-DA)......Page 74
3.3.2 Outside observer’s distribution......Page 77
3.4 NUMERICAL RESULTS......Page 78
REFERENCES......Page 81
4.1 INTRODUCTION......Page 82
4.2 THE GIb/M/1/N MODEL......Page 84
4.3 LATTICE PATH APPROACH......Page 85
4.4.1 Transient Probabilities......Page 86
4.4.2 Counting of Lattice Paths......Page 87
4.4.3 Notations......Page 88
4.5 BUSY PERIOD PROBABILITY FOR THE DISCRETIZED…MODEL......Page 95
4.6 CONTINUOUS…MODEL......Page 98
(i) … model......Page 99
4.8 NUMERICAL COMPUTATIONS AND COMMENTS......Page 100
REFERENCES......Page 102
Part II: Models and Applications......Page 120
5.1 INTRODUCTION......Page 121
5.2 CURRENT MEASURES FOR DISTRIBUTIONAL MORPHOLOGY......Page 122
5.3 (ξ1, ξ2) SYSTEM......Page 125
5.4 ASYMPTOTIC DISTRIBUTIONS OF J1, J2......Page 127
5.5 MISCELLANEOUS REMARKS......Page 129
REFERENCES......Page 131
6.1 INTRODUCTION......Page 134
6.2 INTERPRETATION OF BVG MODEL ASSUMPTIONS......Page 135
6.3 THE MODEL UNDER THE ENVIRONMENTAL EFFECT......Page 137
6.4 DATA ANALYSIS WITH BVG MODEL......Page 138
REFERENCES......Page 142
Part III: Estimation and Testing......Page 143
7.1 INTRODUCTION......Page 144
7.2.1 Area Level Models......Page 146
7.2.2 Unit Level Models......Page 149
7.3 MODEL-BASED INFERENCE......Page 151
7.3.1 EBLUP Method......Page 152
7.3.2 EB Method......Page 155
7.3.3 HB Method......Page 156
Basic models......Page 159
Multivariate models......Page 160
Disease mapping models......Page 161
Multivariate nested error regression models......Page 162
Logistic linear mixed models......Page 163
REFERENCES......Page 164
8.1 INTRODUCTION......Page 171
8.2 EXISTING LITERATURE......Page 173
8.3 MIXTURE OF TWO VON-MISES DISTRIBUTIONS......Page 174
8.4 PRIOR SPECIFICATION......Page 176
8.5 PRIOR AND POSTERIOR PROBABILITY OF UNIMODALITY......Page 177
8.6 THE BAYES FACTOR......Page 178
8.7 APPLICATION......Page 179
8.8 SOME ISSUES......Page 181
REFERENCES......Page 183
9.1 INTRODUCTION......Page 189
9.2 EXAMINING THE LIKELIHOOD FUNCTION......Page 191
9.3 ALGORITHM TO FIND MLE’S......Page 193
9.4 NUMERICAL EXAMPLE......Page 195
REFERENCES......Page 196
10.1 INTRODUCTION......Page 198
10.2.1 Ranked Set Sampling......Page 200
10.2.2 Modified Ranked Set Sampling......Page 201
10.2.3 New Ranked Set Sampling......Page 202
10.3 LAPLACE DISTRIBUTION......Page 203
10.4.1 Joint Estimation of mu and sigma......Page 205
10.4.3 Estimation of sigma......Page 206
REFERENCES......Page 207
11.1 INTRODUCTION......Page 211
11.2 THE MONOTONICITY OF di’s......Page 213
11.3 RESULTS ON ORDERED COMPONENTS OF A RANDOM VECTOR......Page 215
REFERENCES......Page 219
Part IV: Robust Inference......Page 222
12.1 INTRODUCTION......Page 223
12.1.1 A Unifying Structure......Page 224
L-Statistics as statistical functionals......Page 226
GL-statistics as statistical functionals......Page 227
Two examples: Spread measures of Bickel and Lehmann......Page 228
12.3.1 Differentiation Methodology......Page 229
12.3.2 The Estimation Error in the U-Empirical Process......Page 230
12.3.3 Extended Glivenko-Cantelli Theory......Page 231
12.3.4 Oscillation Theory, Generalized Order Statistics, and Bahadur Representations......Page 232
12.3.5 Estimation of the Variance of a U-Statistic......Page 233
12.4.1 Asymptotic Normality and the LIL......Page 234
12.4.3 Large Deviation Theory......Page 235
Location estimation......Page 236
Regression slope estimation......Page 237
Scale......Page 238
12.5.5 Robust Estimation of Exponential Scale Parameter......Page 239
REFERENCES......Page 240
CHAPTER 13: A CLASS OF ROBUST STEPWISE TESTS FOR MANOVA......Page 244
13.1 INTRODUCTION......Page 245
13.2.1 Robust Univariate Tests......Page 247
13.2.2 Combining Independent P-Values......Page 249
13.2.3 Modified Step Down Procedure......Page 250
13.3 ROBUST STEPWISE TESTS......Page 252
13.4.1 The Study......Page 253
REFERENCES......Page 256
14.1 INTRODUCTION......Page 266
14.2.1 General Mixed Linear Model......Page 268
14.2.2 Maximum Likelihood and Restricted Maximum Likelihood Estimators......Page 269
14.2.3 Robust Versions of ML and REML Estimators......Page 270
14.3 DESCRIPTION OF THE SIMULATION EXPERIMENT......Page 271
14.4.3 MSE’s of Estimators of…......Page 273
REFERENCES......Page 274
Part V: Regression and Design......Page 286
CHAPTER 15: PERFORMANCE OF THE PTE BASED ON THE CONFLICTING W, LR AND LM TESTS IN REGRESSION MODEL......Page 287
15.1 INTRODUCTION......Page 288
15.2 THE TESTS AND PROPOSED ESTIMATORS......Page 289
15.3 BIAS, M AND RISK OF THE ESTIMATORS......Page 291
15.4.1 Bias Analysis of the Estimators......Page 293
15.4.2 M Analysis of the Estimators......Page 294
15.4.3 Risk Analysis of the Estimators......Page 295
15.5 EFFICIENCY ANALYSIS AND RECOMMENDATIONS......Page 297
15.6 CONCLUSION......Page 299
REFERENCES......Page 300
CHAPTER 16: ESTIMATION OF REGRESSION AND DISPERSION PARAMETERS IN THE ANALYSIS OF PROPORTIONS......Page 307
16.1 INTRODUCTION......Page 308
16.2.1 The Extended Beta-Binomial Likelihood......Page 309
16.2.2 The Quasi-Likelihood Method......Page 310
16.2.3 Estimation Using Quadratic Estimating Equations......Page 311
16.3 ASYMPTOTIC RELATIVE EFFICIENCY......Page 313
16.4 EXAMPLES......Page 316
16.5 DISCUSSION......Page 317
REFERENCES......Page 318
CHAPTER 17: SEMIPARAMETRIC LOCATION-SCALE REGRESSION MODELS FOR SURVIVAL DATA......Page 328
17.1 INTRODUCTION......Page 329
17.2 LIKELIHOOD FUNCTION FOR THE PARAMETRIC LOCATION-SCALE MODELS......Page 330
17.3.1 Application of Generalized Profile Likelihood to Semiparametric Location-Scale Regression Models......Page 331
17.3.2 Estimation and Large Sample Properties......Page 332
17.4 EXAMPLES OF SEMIPARAMETRIC LOCATION-SCALE REGRESSION MODELS......Page 333
17.5 AN EXAMPLE WITH CENSORED SURVIVAL DATA: PRIMARY BILIARY CIRRHOSIS (PBC) DATA......Page 335
REFERENCES......Page 336
APPENDIX: COMPUTATION OF THE ESTIMATES......Page 337
18.1 INTRODUCTION......Page 348
18.2.1 Orthogonality and Saturation......Page 350
Individual and familywise control of error rates......Page 352
Strong control of error rates......Page 353
18.3.1 Background......Page 354
Closed, step-down tests......Page 356
Iterative methods and sharper critical values: an open problem......Page 358
Directional inference: an open problem......Page 359
18.3.3 Individual Tests......Page 360
18.3.5 Simultaneous Confidence Intervals......Page 361
18.3.6 Adaptive Methods......Page 362
18.4 NON-ORTHOGONAL SATURATED DESIGNS......Page 363
18.4.1 Individual Confidence Intervals......Page 364
18.5 SUPER-SATURATED DESIGNS......Page 365
REFERENCES......Page 366
CHAPTER 19: ON ESTIMATING SUBJECT-TREATMENT INTERACTION......Page 371
19.1 INTRODUCTION......Page 372
19.2 AN ESTIMATOR OF S2D USING CONCOMITANT INFORMATION......Page 374
A general prediction approach......Page 376
19.3 AN ILLUSTRATIVE EXAMPLE......Page 381
19.4 SUMMARY/CONCLUSIONS......Page 382
REFERENCES......Page 383
Part VI: Sample Size and Methodology......Page 387
20.1 ESTABLISHING THERAPEUTIC EQUIVALENCE IN PARALLEL STUDIES......Page 388
20.1.1 Tests under Delta-Formulation (20.1.2)......Page 390
20.1.2 Tests under Relative Risk Formulation (ψ Formulation)......Page 392
Logarithmic transformation......Page 393
20.1.3 Confidence Bound Method for Delta Formulation......Page 394
20.2 SAMPLE SIZE FOR PAIRED DATA STUDIES......Page 395
20.2.1 Testing for Equality of Correlated Proportions......Page 396
Score test......Page 398
Test based on sample proportions......Page 399
A Wald type test......Page 400
REFERENCES......Page 401
21.1 INTRODUCTION......Page 404
21.2 FORMULATION OF THE PROBLEM......Page 406
21.3 THE MAIN RESULTS......Page 407
21.4 FIXED-WIDTH CONFIDENCE INTERVAL ESTIMATION......Page 416
REFERENCES......Page 419
Part VII: Applications to Industry......Page 420
22.1 INTRODUCTION......Page 421
Commitment of management......Page 422
Systems thinking......Page 423
Training considerations......Page 424
Graduate programme......Page 425
22.7 UNIVERSITY OF WATERLOO AND INDUSTRY......Page 426
Co-op students......Page 428
22.8 CONCLUDING REMARKS......Page 429
REFERENCES......Page 430
23.1 INTRODUCTION......Page 432
23.2 DESIGNS FOR CONTROL BASED ON H.P.D. SETS......Page 434
23.3 AN EXAMPLE OF THE USE OF HPD DESIGNS......Page 436
23.4 DESIGNS FOR R.S.B. BASED ON C.P. INTERVALS......Page 437
23.5 CONCLUDING REMARKS......Page 439
APPENDIX: MODEL USED IN SECTION 23.3......Page 440
REFERENCES......Page 441
24.1 INTRODUCTION......Page 443
24.2 THE CLASS......Page 444
24.3.1 Coherent Structures......Page 447
24.3.2 Convolutions......Page 449
24.3.3 Mixtures......Page 451
24.4 THE DISCRETE CLASS…AND ITS DUAL......Page 452
24.5 …AGING WITH SHOCKS......Page 454
REFERENCES......Page 458
25.1 INTRODUCTION......Page 459
25.2.1 Model......Page 461
25.2.2 Modification of Greenberg and Stokes Estimators......Page 462
25.2.3 An Empirical Bayes Estimator......Page 464
25.2.4 Comparison of Estimators......Page 466
25.2.5 Example......Page 468
25.3.1 Estimators......Page 470
25.4 SUGGESTIONS FOR FURTHER RESEARCH......Page 472
Appendix A1.2: Calculations of Probabilities......Page 473
Appendix A2.1: Bias and the MSE Derivation for Ûnew,2abknown......Page 474
Appendix A2.2: MSE of estimators, ÛGS,1, ÛGS,2 or Ûnew,1......Page 476
REFERENCES......Page 477
26.1 THE GE ENVIRONMENT......Page 482
26.2 SIX SIGMA......Page 484
26.3.1 Introduction......Page 485
26.3.3 Reliability Issue with a Supplied Part......Page 486
26.3.4 Constructing a Reliability Database......Page 487
26.4 SOME SURPRISES COMING TO INDUSTRY......Page 488
Recommendations to Students......Page 489
Recommendations to Departments......Page 490
REFERENCES......Page 491
Part VIII: Applications to Ecology, Biology and Health......Page 492
27.1 CERTAIN CHALLENGES AND ADVANCES IN TRANSECT SAMPLING......Page 493
27.1.1 Deep-Sea Red Crab......Page 494
27.1.2 Bivariate Sighting Functions......Page 496
The method......Page 498
27.2.1 Estimating Prevalence Using Composites......Page 502
Asymptotic performance of compositing......Page 503
Optimal composite sample size and its robustness......Page 504
Bias reduction......Page 506
27.2.2 Two-Way Compositing......Page 507
27.2.3 Compositing and Stochastic Monotonicity......Page 508
Pareto distribution......Page 509
27.3.1 Adaptive Sampling and GIS......Page 511
27.3.2 Using Covariate-Species Community Dissimilarity to Guide Sampling......Page 515
REFERENCES......Page 519
28.1 INTRODUCTION......Page 522
28.2 PHYSIOLOGICAL BACKGROUND......Page 523
28.3.1 Moment Methods......Page 525
28.3.2 Intensity Function Based Methods......Page 527
28.3.3 Frequency Domain Methods......Page 528
28.3.4 Graphical Methods......Page 531
28.3.5 Parametric Methods......Page 533
REFERENCES......Page 536
CHAPTER 29: SOME STATISTICAL ISSUES INVOLVING MULTIGENERATION CYTONUCLEAR DATA......Page 540
29.1 INTRODUCTION......Page 541
29.2 NEUTRALITY OR SELECTION?......Page 542
29.2.1 Sampling Schemes for Multi-Generation Data......Page 544
29.2.2 An Omnibus Test......Page 545
29.2.3 Application to Gambusia Data......Page 546
29.2.5 Tests Against a Specific Selection Model......Page 547
Examples of selection schemes......Page 548
Construction of a test statistic......Page 549
Calculation of P-value using bootstrap......Page 551
Power and sample size......Page 552
29.3 INFERENCE FOR THE SELECTION COEFFICIENTS......Page 553
29.3.2 An Approximate Likelihood......Page 554
REFERENCES......Page 556
30.1 INTRODUCTION......Page 562
30.2 CONFIDENCE INTERVALS FOR CER......Page 563
Symmetric interval......Page 564
30.3 COMPARISON OF INTERVALS......Page 565
Specifying distributions and parameters......Page 567
30.5 RESULTS......Page 568
30.6 RECOMMENDATIONS......Page 573
REFERENCES......Page 574
31.1 INTRODUCTION......Page 576
31.2.1 Flowgraph Models for Series Systems......Page 578
31.2.2 Flowgraph Models for Parallel Systems......Page 579
31.2.3 Flowgraph Models with Feedback......Page 580
31.3 RELIABILITY APPLICATION: HYDRAULIC PUMP SYSTEM......Page 581
31.4 SURVIVAL ANALYSIS APPLICATION: A FEED FORWARD MODEL FOR HIV......Page 583
31.5 CONCLUSION......Page 585
REFERENCES......Page 586
Part IX: Applications to Economics and Management......Page 587
32.1 INTRODUCTION......Page 588
32.2.1 The Elements of the IM Test for the Output Model......Page 590
32.2.2 The Elements of the IM Test for the Cost Model......Page 595
32.3.1 Output Model Estimation......Page 597
32.3.2 Moments Test for the Output Model......Page 598
32.3.4 Moments Test for the Cost Model......Page 600
32.4 CONCLUSION......Page 602
APPENDIX A: Derivations of the elements of IM test for the output model......Page 603
APPENDIX B: Derivations of the elements of the IM test for the cost model......Page 605
REFERENCES......Page 608
33.1 THE INTRODUCTION AND MOTIVATION......Page 610
33.2 GLM, GEE & PANEL LOGIT/PROBIT (LDV) MODELS......Page 614
33.2.1 GLM for Panel Data......Page 618
33.2.2 Random Effects Model from Econometrics......Page 619
33.2.3 Derivation of GEE, the Estimator for beta and Standard Errors......Page 620
33.3 GEE ESTIMATION OF CEO TURNOVER AND THREE HYPOTHESES......Page 622
Managerial characteristics......Page 624
Regional variables......Page 625
Customer wealth......Page 626
Turnover and allowed returns......Page 627
Managerial turnover and electricity price changes......Page 628
33.4 CONCLUDING REMARKS......Page 629
REFERENCES......Page 630