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Statistical Models and Methods for Reliability and Survival Analysis

ISBN: 978-1-84821-619-8
416 pages
December 2013, Wiley-ISTE
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Description

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.

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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

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Author Information

Vincent Couallier is Associate Professor at Bordeaux Segalen University in France

Léo Gerville-Réache is Associate Professor at Bordeaux 2 University in France.

Catherine Huber-Carol is Professor Emeritus at Paris René Descartes University in France.

Nikolaos Limnios is Professor at Compiègne University of Technology in France.

Mounir Mesbah is Professor at University Pierre and Marie Curie in Paris, France.

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