Preface xv
Biography of Mikhail Stepanovitch Nikouline xvii
Vincent COUALLIER, L©o GERVILLE-RACHE, Catherine HUBER-CAROL, Nikolaos LIMNIOS and Mounir MESBAH
Part 1. Statistical Models and Methods 1
Chapter 1. Unidimensionality, Agreement and Concordance Probability 3
Zhezhen JIN and Mounir MESBAH
1.1. Introduction 3
1.2. From reliability to unidimensionality: CAC and curve 4
1.2.1. Classical unidimensional models for measurement 4
1.2.2. Reliability of an instrument: CAC 6
1.2.3. Unidimensionality of an instrument: BRC 9
1.3. Agreement between binary outcomes: the kappa coefficient 10
1.3.1. The kappa model 10
1.3.2. The kappa coefficient 10
1.3.3. Estimation of the kappa coefficient 10
1.4. Concordance probability 11
1.4.1. Relationship with Kendallâs Ï measure 12
1.4.2. Relationship with Somerâs D measure 12
1.4.3. Relationship with ROC curve 13
1.5. Estimation and inference 14
1.6. Measure of agreement 14
1.7. Extension to survival data 15
1.7.1. Harrellâs c-index 15
1.7.2. Measure of discriminatory power 16
1.8. Discussion 17
1.9. Bibliography 18
Chapter 2. A Universal Goodness-of-Fit Test Based on Regression Techniques 21
Florence GEORGE and Sneh GULATI
2.1. Introduction 21
2.2. The Brain and Shapiro procedure for the exponential distribution 22
2.3. Applications of the Brain and Shapiro test 24
2.4. Small sample null distribution of the test statistic for specific distributions 25
2.5. Power studies 28
2.6. Some real examples 28
2.7. Conclusions 31
2.8. Acknowledgment 32
2.9. Bibliography 32
Chapter 3. Entropy-type Goodness-of-Fit Tests for Heavy-Tailed Distributions 33
Andreas MAKRIDES, Alex KARAGRIGORIOU and Filia VONTA
3.1. Introduction 33
3.2. The entropy test for heavy-tailed distributions 35
3.2.1. Development and asymptotic theory 35
3.2.2. Discussion 39
3.3. Simulation study 40
3.4. Conclusions 42
3.5. Bibliography 42
Chapter 4. Penalized Likelihood Methodology and Frailty Models 45
Emmanouil ANDROULAKIS, Christos KOUKOUVINOS and Filia VONTA
4.1. Introduction 45
4.2. Penalized likelihood in frailty models for clustered data 48
4.2.1. Gamma distributed frailty 52
4.2.2. Inverse Gaussian distributed frailty 52
4.2.3. Uniform distributed frailty 54
4.3. Simulation results 55
4.4. Concluding remarks 57
4.5. Bibliography 57
Chapter 5. Interactive Investigation of Statistical Regularities in Testing Composite Hypotheses of Goodness of Fit 61
Boris LEMESHKO, Stanislav LEMESHKO and Andrey ROGOZHNIKOV
5.1. Introduction 61
5.2. Distributions of the test statistics in the case of testing composite hypotheses 63
5.3. Testing composite hypotheses in âreal-timeâ 68
5.4. Conclusions 73
5.5. Acknowledgment 73
5.6. Bibliography 73
Chapter 6. Modeling of Categorical Data 77
Henning LUTER
6.1. Introduction 77
6.2. Continuous conditional distributions 78
6.2.1. Conditional normal distribution 78
6.2.1.1. Estimation of parameters 78
6.2.2. More general continuous conditional distributions 81
6.2.2.1. Conditional distribution 82
6.2.2.2. Normal copula 83
6.3. Discrete conditional distributions 84
6.3.1. Parametric conditional distributions 84
6.3.2. Estimation of parameters 86
6.4. Goodness of fit 86
6.4.1. Distribution of ËX2 87
6.5. Modeling of categorical data 88
6.5.1. Contingency tables 89
6.5.1.1. General tables 89
6.5.1.2. Further examples 93
6.6. Bibliography 93
Chapter 7. Within the Sample Comparison of Prediction Performance of Models and Submodels: Application to Alzheimerâs Disease 95
Catherine HUBER-CAROL, Shulamith T. GROSS and Annick ALPROVITCH
7.1. Introduction 95
7.2. Framework 96
7.2.1. General description of the data set and the models to be compared 96
7.2.2. Definition of the performance prediction criteria: IDI and BRI 96
7.3. Estimation of IDI and BRI 97
7.3.1. General estimating equations for IDI and BRI 98
7.3.2. Estimation of IDI and BRI in the logistic case 98
7.3.2.1. Asymptotics of IDI2/1 for logistic predictors 99
7.3.2.2. Asymptotics of BRI2/1 for logistic predictors 100
7.4. Simulation studies 102
7.4.1. First simulation 102
7.4.2. Second simulation: Gu and Pepeâs example 104
7.5. The three city study of Alzheimerâs disease 106
7.6. Conclusion 108
7.7. Bibliography 109
Chapter 8. Durbinâ"Knott Components and Transformations of the Cram©r-von Mises Test 111
Gennady MARTYNOV
8.1. Introduction 111
8.2. Weighted Cram©r-von Mises statistic 111
8.3. Examples of the Cram©r-von Mises statistics 113
8.3.1. Classical Cram©r-von Mises statistic 113
8.3.2. Andersonâ"Darling statistic 113
8.3.3. Cram©r-von Mises statistic with the power weight function 114
8.4. Weighted parametric Cram©r-von Mises statistic 114
8.4.1. Covariance functions of weighted parametric empirical process 114
8.4.2. Eigenvalues and eigenfunctions for weighted parametric Cram©rvon Mises statistic 116
8.5. Transformations of the Cram©r-von Mises statistic 117
8.5.1. Preliminary notes 117
8.5.2. Replacement of eigenvalues 118
8.5.3. Transformed statistics 119
8.6. Bibliography 122
Chapter 9. Conditional Inference in Parametric Models 125
Michel BRONIATOWSKI and Virgile CARON
9.1. Introduction and context 125
9.2. The approximate conditional density of the sample 127
9.2.1. Approximation of conditional densities 127
9.2.2. The proxy of the conditional density of the sample 129
9.2.3. Comments on implementation 131
9.3. Sufficient statistics and approximated conditional density 131
9.3.1. Keeping sufficiency under the proxy density 131
9.3.2. Raoâ"Blackwellization 132
9.4. Exponential models with nuisance parameters 135
9.4.1. Conditional inference in exponential families 135
9.4.2. Application of conditional sampling to MC tests 137
9.4.2.1. Context 137
9.4.2.2. Bimodal likelihood: testing the mean of a normal distribution in dimension 2 139
9.4.3. Estimation through conditional likelihood 140
9.5. Bibliography 142
Chapter 10. On Testing Stochastic Dominance by Exceedance, Precedence and Other Distribution-Free Tests, with Applications 145
Paul DEHEUVELS
10.1. Introduction 145
10.2. Results 148
10.2.1. The experimental data set 148
10.2.2. An application of the Wilcoxonâ"Mannâ"Whitney statistics 149
10.2.3. One-sided Kolmogorov-Smirnov tests 150
10.2.4. Precedence and Exceedance Tests. 152
10.3. Negative binomial limit laws 155
10.4. Conclusion 159
10.5. Bibliography 159
Chapter 11. Asymptotically Parameter-Free Tests for Ergodic Diffusion Processes 161
Yury A. KUTOYANTS and Li ZHOU
11.1. Introduction 161
11.2. Ergodic diffusion process and some limits 165
11.3. Shift parameter 168
11.4. Shift and scale parameters 172
11.5. Bibliography 175
Chapter 12. A Comparison of Homogeneity Tests for Different Alternative Hypotheses 177
Sergey POSTOVALOV and Petr PHILONENKO
12.1. Homogeneity tests 178
12.1.1. Tests for data without censoring 179
12.1.2. Tests for data with censoring 180
12.2. Alternative hypotheses 184
12.3. Power simulation 185
12.3.1. Power of tests without censoring 187
12.3.2. Power of tests with censoring 189
12.3.2.1. How does the distribution of censoring time affect the power of the test? 189
12.3.2.2. How does the censoring rate affect the power of the test? 191
12.4. Statistical inference 191
12.5. Acknowledgment 192
12.6. Bibliography 193
Chapter 13. Some Asymptotic Results for Exchangeably Weighted Bootstraps of the Empirical Estimator of a Semi-Markov Kernel with Applications 195
Salim BOUZEBDA and Nikolaos LIMNIOS
13.1. Introduction 195
13.2. Semi-Markov setting 197
13.3. Main results 201
13.4. Bootstrap for a multidimensional empirical estimator of a continuous-time semi-Markov kernel 205
13.5. Confidence intervals 208
13.6. Bibliography 210
Chapter 14. On Chi-Squared Goodness-of-Fit Test for Normality 213
Mikhail NIKULIN, L©o GERVILLE-RACHE and Xuan Quang TRAN
14.1. Chiâ"squared test for normality 213
14.2. Simulation study 221
14.3. Bibliography 226
Part 2. Statistical Models and Methods in Survival Analysis 229
Chapter 15. Estimation/Imputation Strategies for Missing Data in Survival Analysis 231
Elodie BRUNEL, Fabienne COMTE and Agathe GUILLOUX
15.1. Introduction 231
15.2. Model and strategies 233
15.2.1. Model assumptions 233
15.2.2. Strategy involving knowledge of ζ 234
15.2.3. Strategy involving knowledge of Ï 235
15.2.4. Estimation of ζ or Ï: logit or non-parametric regression 236
15.2.5. Computing the hazard estimators 236
15.2.6. Theoretical results 239
15.3. Imputation-based strategy 241
15.4. Numerical comparison 242
15.5. Proofs 244
15.6. Bibliography 251
Chapter 16. Non-Parametric Estimation of Linear Functionals of a Multivariate Distribution Under Multivariate Censoring with Applications 253
Olivier LOPEZ and Philippe SAINT-PIERRE
16.1. Introduction 253
16.2. Non-parametric estimation of the distribution 255
16.3. Asymptotic properties 257
16.4. Statistical applications of functionals 260
16.4.1. Dependence measures 260
16.4.2. Bootstrap 261
16.4.3. Linear regression 262
16.5. Illustration 263
16.6. Conclusion 264
16.7. Acknowledgment 264
16.8. Bibliography 264
Chapter 17. Kernel Estimation of Density from Indirect Observation 267
Valentin SOLEV
17.1. Introduction 267
17.1.1. Random partition 267
17.1.2. Indirect observation 268
17.1.3. Kernel density estimator 269
17.2. Density of random vector Î(X) 271
17.3. Pseudo-kernel density estimator 273
17.3.1. Pointwise density estimation based on indirect data 273
17.3.2. Bias of the kernel estimator 274
17.3.3. Estimate of variance 276
17.4. Bibliography 279
Chapter 18. A Comparative Analysis of Some Chi-Square Goodness-of-Fit Tests for Censored Data 281
Ekaterina CHIMITOVA and Boris LEMESHKO
18.1. Introduction 281
18.2. Chi-square goodness-of-fit tests for censored data 283
18.2.1. NRR Ï2 test 283
18.2.2. GPF Ï2 test 284
18.3. The choice of grouping intervals 285
18.3.1. Equifrequent grouping (EFG) 289
18.3.2. Intervals with equal expected numbers of failures (EENFG) 289
18.3.3. Optimal grouping (OptG) 289
18.4. Empirical power study 290
18.5. Conclusions 293
18.6. Acknowledgment 294
18.7. Bibliography 294
Chapter 19. A Non-parametric Test for Comparing Treatments with Missing Data and Dependent Censoring 297
Amel MEZAOUER, Kamal BOUKHETALA and Jean-Fran§ois DUPUY
19.1. Introduction 297
19.2. The proposed test statistic 299
19.3. Asymptotic distribution of the proposed test statistic 301
19.4. Acknowledgment 305
19.5. Appendix 306
19.6. Bibliography 309
Chapter 20. Group Sequential Tests for Treatment Effect with Covariates Adjustment through Simple Cross-Effect Models 311
Isaac Wu HONG-DAR
20.1. Introduction 311
20.2. Notations and models 313
20.3. Group sequential test 316
20.4. Discussion 318
20.5. Acknowledgment 318
20.6. Bibliography 318
Part 3. Reliability and Maintenance 321
Chapter 21. Optimal Maintenance in Degradation Processes 323
Waltraud KAHLE
21.1. Introduction 323
21.2. The degradation model 324
21.3. Optimal replacement after an inspection 326
21.4. The simulation of degradation processes 327
21.5. Shape of cost functions and optimal δ and a 329
21.6. Incomplete preventive maintenance 330
21.7. Bibliography 333
Chapter 22. Planning Accelerated Destructive Degradation Tests with Competing Risks 335
Ying SHI and William Q. MEEKER
22.1. Introduction 336
22.1.1. Background 336
22.1.2. Motivation: adhesive bond C 336
22.1.3. Related literature 337
22.1.4. Overview 338
22.2. Degradation models with competing risks 338
22.2.1. Accelerated degradation model for the primary response 338
22.2.2. Accelerated degradation model for the competing response 339
22.2.3. Degradation models for adhesive bond C 339
22.2.4. Degradation distribution and quantiles 340
22.3. Failure-time distribution with competing risks 341
22.3.1. Relationship between degradation and failure 341
22.3.2. Failure-time distribution and quantiles 342
22.4. Test planning with competing risks 342
22.4.1. ADDT planning information 342
22.4.2. Criterion for ADDT planning with competing risks 343
22.5. ADDT plans with competing risks 344
22.5.1. Initial optimum ADDT plan with competing risks 344
22.5.2. Constrained optimum ADDT plan with competing risks 348
22.5.3. General equivalence theorem 348
22.5.4. Compromise ADDT plan with competing risks 350
22.6. Monte Carlo simulation to evaluate test plans 352
22.7. Conclusions and extensions 353
22.8. Appendix: technical details 354
22.8.1. The Fisher information matrix for ADDT with competing risks 354
22.8.2. Large-sample approximate variance of ht (tp) and tp 355
22.9. Bibliography 355
Chapter 23. A New Goodness-of-Fit Test for Shape-Scale Families 357
Vilijandas BAGDONAVIIUS
23.1. Introduction 357
23.2. The test statistic 358
23.3. The asymptotic distribution of the test statistic 359
23.4. The test 364
23.5. Weibull distribution 364
23.6. Loglogistic distribution 365
23.7. Lognormal distribution 366
23.8. Bibliography 367
Chapter 24. Time-to-Failure of Markov-Modulated Gamma Process with Application to Replacement Policies 369
Christian PAROISSIN and Landy RABEHASAINA
24.1. Introduction 369
24.2. Degradation model 370
24.2.1. Covariate process 370
24.2.2. Degradation process 371
24.3. Time-to-failure distribution 371
24.3.1. Case of a non-modulated gamma process 372
24.3.2. Case of a Markov-modulated gamma process 373
24.3.3. Stochastic comparison 374
24.4. Replacement policies 376
24.4.1. Block replacement policy 377
24.4.2. Age replacement policy 379
24.5. Conclusion 381
24.6. Acknowledgment 381
24.7. Bibliography 382
Chapter 25. Calculation of the Redundant Structure Reliability for Agingtype Elements 383
Alexandr ANTONOV, Alexandr PLYASKIN and Khizri TATAEV
25.1. Introduction 383
25.2. The operation process of the renewal and repaired products 384
25.3. The model of the geometric process 386
25.4. Task solution 387
25.5. Conclusion 389
25.6. Bibliography 390
Chapter 26. On Engineering Risks of Complex Hierarchical Systems Analysis 391
Vladimir RYKOV
26.1. Introduction 391
26.2. Risk definition and measurement 392
26.3. Engineering risk 393
26.4. Risk characteristics for general model calculation 395
26.4.1. Lifelength and appropriate loss size CDF 395
26.4.2. Probability of risk event evolution 396
26.4.3. Lifelength and loss moments 397
26.4.4. Mostly dangerous paths of risk event evolution and sensitivity analysis 399
26.5. Risk analysis for short-time risk models 400
26.6. Conclusion 402
26.7. Bibliography 402
List of Authors 405
Index 409
