Statistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts - Statistical Models and Methods, Statistical Models and Methods in Survival Analysis, and Reliability and Maintenance. The book is intended for researchers interested in statistical methodology and models useful in survival analysis, system reliability and statistical testing for censored and non-censored data.
Table of Contents:
Preface xv
Biography of Mikhail Stepanovitch Nikouline xvii
Vincent COUALLIER, Léo GERVILLE-RÉACHE, 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
1.3. Agreement between binary outcomes: the kappa coefficient 10
1.4. Concordance probability 11
1.5. Estimation and inference 14
1.6. Measure of agreement 14
1.7. Extension to survival data 15
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
3.3. 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
4.3. 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 “real-time” 68
5.4. Conclusions 73
5.5. Acknowledgment 73
5.6. Bibliography 73
Chapter 6. Modeling of Categorical Data 77
Henning LÄUTER
6.1. Introduction 77
6.2. Continuous conditional distributions 78
6.3. Discrete conditional distributions 84
6.4. Goodness of fit 86
6.5. Modeling of categorical data 88
6.6. Bibliography 93
Chapter 7. Within the Sample Comparison of Prediction Performance of Models and Submodels: Application to Alzheimer’s Disease 95
Catherine HUBER-CAROL, Shulamith T. GROSS and Annick ALPÉROVITCH
7.1. Introduction 95
7.2. Framework 96
7.3. Estimation of IDI and BRI 97
7.4. Simulation studies 102
7.5. The three city study of Alzheimer’s disease 106
7.6. Conclusion 108
7.7. Bibliography 109
Chapter 8. Durbin–Knott Components and Transformations of the Cramér-von Mises Test 111
Gennady MARTYNOV
8.1. Introduction 111
8.2. Weighted Cramér-von Mises statistic 111
8.3. Examples of the Cramér-von Mises statistics 113
8.4. Weighted parametric Cramér-von Mises statistic 114
8.5. Transformations of the Cramér-von Mises statistic 117
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
9.3. Sufficient statistics and approximated conditional density 131
9.4. Exponential models with nuisance parameters 135
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
10.3. 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
12.2. Alternative hypotheses 184
12.3. Power simulation 185
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 continuoustime 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, Léo GERVILLE-RÉACHE and Xuan Quang TRAN
14.1. Chi–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
15.3. 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
16.5. 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
17.2. Density of random vector Λ(X) 271
17.3. Pseudo-kernel density estimator 273
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
18.3. The choice of grouping intervals 285
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-François 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
22.2. Degradation models with competing risks 338
22.3. Failure-time distribution with competing risks 341
22.4. Test planning with competing risks 342
22.5. ADDT plans with competing risks 344
22.6. Monte Carlo simulation to evaluate test plans 352
22.7. Conclusions and extensions 353
22.8. Appendix: technical details 354
22.9. Bibliography 355
Chapter 23. A New Goodness-of-Fit Test for Shape-Scale Families 357
Vilijandas BAGDONAVIC¡IUS
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
24.3. Time-to-failure distribution 371
24.4. Replacement policies 376
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
26.5. Risk analysis for short-time risk models 400
26.6. Conclusion 402
26.7. Bibliography 402
List of Authors 405
Index 409
