Preface                                            xv
Biography of Mikhail Stepanovitch Nikouline        xvii
          Vincent Couallier
          L駮 Gerville-R饌che
          Catherine Huber-Carol
          Nikolaos Limnios
          Mounir Mesbah
Part 1. Statistical Models And Methods             1   (228)
  Chapter 1 Unidimensionality, Agreement and       3   (18)
  Concordance Probability
          Zhezhen Jin
          Mounir Mesbah
      1.1 Introduction                             3   (1)
      1.2 From reliability to                      4   (6)
      unidimensionality: CAC and curve
        1.2.1 Classical unidimensional models      4   (2)
        for measurement
        1.2.2 Reliability of an instrument: CAC    6   (3)
        1.2.3 Unidimensionality of an              9   (1)
        instrument: BRC
      1.3 Agreement between binary outcomes:       10  (1)
      the kappa coefficient
        1.3.1 The kappa model                      10  (1)
        1.3.2 The kappa coefficient                10  (1)
        1.3.3 Estimation of the kappa              10  (1)
        coefficient
      1.4 Concordance probability                  11  (3)
        1.4.1 Relationship with Kendall's τ    12  (1)
        measure
        1.4.2 Relationship with Somer's D          12  (1)
        measure
        1.4.3 Relationship with ROC curve          13  (1)
      1.5 Estimation and inference                 14  (1)
      1.6 Measure of agreement                     14  (1)
      1.7 Extension to survival data               15  (2)
        1.7.1 Harrell's c-index                    15  (1)
        1.7.2 Measure of discriminatory power      16  (1)
      1.8 Discussion                               17  (1)
      1.9 Bibliography                             18  (3)
  Chapter 2 A Universal Goodness-of-Fit Test       21  (12)
  Based on Regression Techniques
          Florence George
          Sneh Gulati
      2.1 Introduction                             21  (1)
      2.2 The Brain and Shapiro procedure for      22  (2)
      the exponential distribution
      2.3 Applications of the Brain and Shapiro    24  (1)
      test
      2.4 Small sample null distribution of the    25  (3)
      test statistic for specific distributions
      2.5 Power studies                            28  (1)
      2.6 Some real examples                       28  (3)
      2.7 Conclusions                              31  (1)
      2.8 Acknowledgment                           32  (1)
      2.9 Bibliography                             32  (1)
  Chapter 3 Entropy-type Goodness-of-Fit Tests     33  (12)
  for Heavy-Tailed Distributions
          Andreas Makrides
          Alex Karagrigoriou
          Filia Vonta
      3.1 Introduction                             33  (2)
      3.2 The entropy test for heavy-tailed        35  (5)
      distributions
        3.2.1 Development and asymptotic theory    35  (4)
        3.2.2 Discussion                           39  (1)
      3.3 Simulation study                         40  (2)
      3.4 Conclusions                              42  (1)
      3.5 Bibliography                             42  (3)
  Chapter 4 Penalized Likelihood Methodology       45  (16)
  and Frailty Models
          Emmanouil Androulakis
          Christos Koukouvinos
          Filia Vonta
      4.1 Introduction                             45  (3)
      4.2 Penalized likelihood in frailty          48  (7)
      models for clustered data
        4.2.1 Gamma distributed frailty            52  (1)
        4.2.2 Inverse Gaussian distributed         52  (2)
        frailty
        4.2.3 Uniform distributed frailty          54  (1)
      4.3 Simulation results                       55  (2)
      4.4 Concluding remarks                       57  (1)
      4.5 Bibliography                             57  (4)
  Chapter 5 Interactive Investigation of           61  (16)
  Statistical Regularities in Testing Composite
  Hypotheses of Goodness of Fit
          Boris Lemeshko
          Stanislav Lemeshko
          Andrey Rogozhnikov
      5.1 Introduction                             61  (2)
      5.2 Distributions of the test statistics     63  (5)
      in the case of testing composite
      hypotheses
      5.3 Testing composite hypotheses in          68  (5)
      "real-time"
      5.4 Conclusions                              73  (1)
      5.5 Acknowledgment                           73  (1)
      5.6 Bibliography                             73  (4)
  Chapter 6 Modeling of Categorical Data           77  (18)
          Henning L舫ter
      6.1 Introduction                             77  (1)
      6.2 Continuous conditional distributions     78  (6)
        6.2.1 Conditional normal distribution      78  (1)
        6.2.1.1 Estimation of parameters           78  (3)
        6.2.2 More general continuous              81  (1)
        conditional distributions
        6.2.2.1 Conditional distribution           82  (1)
        6.2.2.2 Normal copula                      83  (1)
      6.3 Discrete conditional distributions       84  (2)
        6.3.1 Parametric conditional               84  (2)
        distributions
        6.3.2 Estimation of parameters             86  (1)
      6.4 Goodness of fit                          86  (2)
        6.4.1 Distribution of χｲ               87  (1)
      6.5 Modeling of categorical data             88  (5)
        6.5.1 Contingency tables                   89  (1)
        6.5.1.1 General tables                     89  (1)
        6.5.1.2 Further examples                   93  (1)
      6.6 Bibliography                             93  (2)
  Chapter 7 Within the Sample Comparison of        95  (16)
  Prediction Performance of Models and
  Submodels: Application to Alzheimer's Disease
          Catherine Huber-Carol
          Shulamith T. Gross
          Annick Alp駻ovitch
      7.1 Introduction                             95  (1)
      7.2 Framework                                96  (1)
        7.2.1 General description of the data      96  (1)
        set and the models to be compared
        7.2.2 Definition of the performance        96  (1)
        prediction criteria: IDI and BRI
      7.3 Estimation of IDI and BRI                97  (5)
        7.3.1 General estimating equations for     98  (1)
        IDI and BRI
        7.3.2 Estimation of IDI and BRI in the     98  (1)
        logistic case
        7.3.2.1 Asymptotics of IDI2/1 for          99  (1)
        logistic predictors
        7.3.2.2 Asymptotics of BRI/2/1 for         100 (2)
        logistic predictors
      7.4 Simulation studies                       102 (4)
        7.4.1 First simulation                     102 (2)
        7.4.2 Second simulation: Gu and Pepe's     104 (2)
        example
      7.5 The three city study of Alzheimer's      106 (2)
      disease
      7.6 Conclusion                               108 (1)
      7.7 Bibliography                             109 (2)
  Chapter 8 Durbin-Knott Components and            111 (14)
  Transformations of the Cram駻-von Mises Test
          Gennady Martynov
      8.1 Introduction                             111 (1)
      8.2 Weighted Cram駻-von Mises statistic      111 (2)
      8.3 Examples of the Cram駻-von Mises         113 (1)
      statistics
        8.3.1 Classical Cram駻-von Mises           113 (1)
        statistic
        8.3.2 Anderson-Darling statistic           113 (1)
        8.3.3 Cram駻-von Mises statistic with      114 (1)
        the power weight function
      8.4 Weighted parametric Cram駻-von Mises     114 (3)
      statistic
        8.4.1 Covariance functions of weighted     114 (2)
        parametric empirical process
        8.4.2 Eigenvalues and eigenfunctions       116 (1)
        for weighted parametric Cram駻-von
        Mises statistic
      8.5 Transformations of the Cram駻-von        117 (5)
      Mises statistic
        8.5.1 Preliminary notes                    117 (1)
        8.5.2 Replacement of eigenvalues           118 (1)
        8.5.3 Transformed statistics               119 (3)
      8.6 Bibliography                             122 (3)
  Chapter 9 Conditional Inference in Parametric    125 (20)
  Models
          Michel Broniatowski
          Virgile Caron
      9.1 Introduction and context                 125 (2)
      9.2 The approximate conditional density      127 (4)
      of the sample
        9.2.1 Approximation of conditional         127 (2)
        densities
        9.2.2 The proxy of the conditional         129 (2)
        density of the sample
        9.2.3 Comments on implementation           131 (1)
      9.3 Sufficient statistics and                131 (4)
      approximated conditional density
        9.3.1 Keeping sufficiency under the        131 (1)
        proxy density
        9.3.2 Rao-Blackwellization                 132 (3)
      9.4 Exponential models with nuisance         135 (7)
      parameters
        9.4.1 Conditional inference in             135 (2)
        exponential families
        9.4.2 Application of conditional           137 (1)
        sampling to MC tests
        9.4.2.1 Context                            137 (1)
        9.4.2.2 Bimodal likelihood: testing the    139 (1)
        mean of a normal distribution in
        dimension 2
        9.4.3 Estimation through conditional       140 (2)
        likelihood
      9.5 Bibliography                             142 (3)
  Chapter 10 On Testing Stochastic Dominance by    145 (16)
  Exceedance, Precedence and Other
  Distribution-Free Tests, with Applications
          Paul Deheuvels
      10.1 Introduction                            145 (3)
      10.2 Results                                 148 (7)
        10.2.1 The experimental data set           148 (1)
        10.2.2 An application of the               149 (1)
        Wilcoxon-Mann-Whitney statistics
        10.2.3 One-sided Kolmogorov-Smirnov        150 (2)
        tests
        10.2.4 Precedence and Exceedance Tests     152 (3)
      10.3 Negative binomial limit laws            155 (4)
      10.4 Conclusion                              159 (1)
      10.5 Bibliography                            159 (2)
  Chapter 11 Asymptotically Parameter-Free         161 (16)
  Tests for Ergodic Diffusion Processes
          Yury A. Kutoyants
          Li Zhou
      11.1 Introduction                            161 (4)
      11.2 Ergodic diffusion process and some      165 (3)
      limits
      11.3 Shift parameter                         168 (4)
      11.4 Shift and scale parameters              172 (3)
      11.5 Bibliography                            175 (2)
  Chapter 12 A Comparison of Homogeneity Tests     177 (18)
  for Different Alternative Hypotheses
          Sergey Postovalov
          Petr Philonenko
      12.1 Homogeneity tests                       178 (6)
        12.1.1 Tests for data without censoring    179 (1)
        12.1.2 Tests for data with censoring       180 (4)
      12.2 Alternative hypotheses                  184 (1)
      12.3 Power simulation                        185 (6)
        12.3.1 Power of tests without censoring    187 (2)
        12.3.2 Power of tests with censoring       189 (1)
        12.3.2.1 How does the distribution of      189 (1)
        censoring time affect the power of the
        test?
        12.3.2.2 How does the censoring rate       191 (1)
        affect the power of the test?
      12.4 Statistical inference                   191 (1)
      12.5 Acknowledgment                          192 (1)
      12.6 Bibliography                            193 (2)
  Chapter 13 Some Asymptotic Results for           195 (18)
  Exchangeably Weighted Bootstraps of the
  Empirical Estimator of a Semi-Markov Kernel
  with Applications
          Salim Bouzebda
          Nikolaos Limnios
      13.1 Introduction                            195 (2)
      13.2 Semi-Markov setting                     197 (4)
      13.3 Main results                            201 (4)
      13.4 Bootstrap for a multidimensional        205 (3)
      empirical estimator of a continuous- time
      semi-Markov kernel
      13.5 Confidence intervals                    208 (2)
      13.6 Bibliography                            210 (3)
  Chapter 14 On Chi-Squared Goodness-of-Fit        213 (16)
  Test for Normality
          Mikhail Nikulin
          L駮 Gerville-R饌che
          Xuan Quang Tran
      14.1 Chi-squared test for normality          213 (8)
      14.2 Simulation study                        221 (5)
      14.3 Bibliography                            226 (3)
Part 2 Statistical Models And Methods In           229 (92)
Survival Analysis
  Chapter 15 Estimation/Imputation Strategies      231 (22)
  for Missing Data in Survival Analysis
          Elodie Brunel
          Fabienne Comte
          Agathe Guilloux
      15.1 Introduction                            231 (2)
      15.2 Model and strategies                    233 (8)
        15.2.1 Model assumptions                   233 (1)
        15.2.2 Strategy involving knowledge of     234 (1)
        ζ
        15.2.3 Strategy involving knowledge of     235 (1)
        π
        15.2.4 Estimation of ζ or π:       236 (1)
        logit or non-parametric regression
        15.2.5 Computing the hazard estimators     236 (3)
        15.2.6 Theoretical results                 239 (2)
      15.3 Imputation-based strategy               241 (1)
      15.4 Numerical comparison                    242 (2)
      15.5 Proofs                                  244 (7)
      15.6 Bibliography                            251 (2)
  Chapter 16 Non-Parametric Estimation of          253 (14)
  Linear Functionals of a Multivariate
  Distribution Under Multivariate Censoring
  with Applications
          Olivier Lopez
          Philippe Saint-Pierre
      16.1 Introduction                            253 (2)
      16.2 Non-parametric estimation of the        255 (2)
      distribution
      16.3 Asymptotic properties                   257 (3)
      16.4 Statistical applications of             260 (3)
      functionals
        16.4.1 Dependence measures                 260 (1)
        16.4.2 Bootstrap                           261 (1)
        16.4.3 Linear regression                   262 (1)
      16.5 Illustration                            263 (1)
      16.6 Conclusion                              264 (1)
      16.7 Acknowledgment                          264 (1)
      16.8 Bibliography                            264 (3)
  Chapter 17 Kernel Estimation of Density from     267 (14)
  Indirect Observation
          Valentin Solev
      17.1 Introduction                            267 (4)
        17.1.1 Random partition                    267 (1)
        17.1.2 Indirect observation                268 (1)
        17.1.3 Kernel density estimator            269 (2)
      17.2 Density of random vector Λ(X)    271 (2)
      17.3 Pseudo-kernel density estimator         273 (6)
        17.3.1 Pointwise density estimation        273 (1)
        based on indirect data
        17.3.2 Bias of the kernel estimator        274 (2)
        17.3.3 Estimate of variance                276 (3)
      17.4 Bibliography                            279 (2)
  Chapter 18 A Comparative Analysis of Some        281 (16)
  Chi-Square Goodness-of-Fit Tests for Censored
  Data
          Ekaterina Chimitova
          Boris Lemeshko
      18.1 Introduction                            281 (2)
      18.2 Chi-square goodness-of-fit tests for    283 (2)
      censored data
        18.2.1 NRR Χｲ test                     283 (1)
        18.2.2 GPF Χｲ test                     284 (1)
      18.3 The choice of grouping intervals        285 (5)
        18.3.1 Equifrequent grouping (EFG)         289 (1)
        18.3.2 Intervals with equal expected       289 (1)
        numbers of failures (EENFG)
        18.3.3 Optimal grouping (OptG)             289 (1)
      18.4 Empirical power study                   290 (3)
      18.5 Conclusions                             293 (1)
      18.6 Acknowledgment                          294 (1)
      18.7 Bibliography                            294 (3)
  Chapter 19 A Non-parametric Test for             297 (14)
  Comparing Treatments with Missing Data and
  Dependent Censoring
          Amel Mezaouer
          Kamal Boukhetala
          Jean-Fran輟is Dupuy
      19.1 Introduction                            297 (2)
      19.2 The proposed test statistic             299 (2)
      19.3 Asymptotic distribution of the          301 (4)
      proposed test statistic
      19.4 Acknowledgment                          305 (1)
      19.5 Appendix                                306 (3)
      19.6 Bibliography                            309 (2)
  Chapter 20 Group Sequential Tests for            311 (10)
  Treatment Effect with Covariates Adjustment
  through Simple Cross-Effect Models
          Isaac Wu Hong-Dar
      20.1 Introduction                            311 (2)
      20.2 Notations and models                    313 (3)
      20.3 Group sequential test                   316 (2)
      20.4 Discussion                              318 (1)
      20.5 Acknowledgment                          318 (1)
      20.6 Bibliography                            318 (3)
Part 3 Reliability And Maintenance                 321 (84)
  Chapter 21 Optimal Maintenance in Degradation    323 (12)
  Processes
          Waltraud Kahle
      21.1 Introduction                            323 (1)
      21.2 The degradation model                   324 (2)
      21.3 Optimal replacement after an            326 (1)
      inspection
      21.4 The simulation of degradation           327 (2)
      processes
      21.5 Shape of cost functions and optimal     329 (1)
      δ and α
      21.6 Incomplete preventive maintenance       330 (3)
      21.7 Bibliography                            333 (2)
  Chapter 22 Planning Accelerated Destructive      335 (22)
  Degradation Tests with Competing Risks
          Ying Shi
          William Q. Meeker
      22.1 Introduction                            336 (2)
        22.1.1 Background                          336 (1)
        22.1.2 Motivation: adhesive bond C         336 (1)
        22.1.3 Related literature                  337 (1)
        22.1.4 Overview                            338 (1)
      22.2 Degradation models with competing       338 (3)
      risks
        22.2.1 Accelerated degradation model       338 (1)
        for the primary response
        22.2.2 Accelerated degradation model       339 (1)
        for the competing response
        22.2.3 Degradation models for adhesive     339 (1)
        bond C
        22.2.4 Degradation distribution and        340 (1)
        quantiles
      22.3 Failure-time distribution with          341 (1)
      competing risks
        22.3.1 Relationship between degradation    341 (1)
        and failure
        22.3.2 Failure-time distribution and       342 (1)
        quantiles
      22.4 Test planning with competing risks      342 (2)
        22.4.1 ADDT planning information           342 (1)
        22.4.2 Criterion for ADDT planning with    343 (1)
        competing risks
      22.5 ADDT plans with competing risks         344 (8)
        22.5.1 Initial optimum ADDT plan with      344 (4)
        competing risks
        22.5.2 Constrained optimum ADDT plan       348 (1)
        with competing risks
        22.5.3 General equivalence theorem         348 (2)
        22.5.4 Compromise ADDT plan with           350 (2)
        competing risks
      22.6 Monte Carlo simulation to evaluate      352 (1)
      test plans
      22.7 Conclusions and extensions              353 (1)
      22.8 Appendix: technical details             354 (1)
        22.8.1 The Fisher information matrix       354 (1)
        for ADDT with competing risks
        22.8.2 Large-sample approximate            355 (1)
        variance of ht (tp) and tp
      22.9 Bibliography                            355 (2)
  Chapter 23 A New Goodness-of-Fit Test for        357 (12)
  Shape-Scale Families
          Vilijandas Bagdonavicius
      23.1 Introduction                            357 (1)
      23.2 The test statistic                      358 (1)
      23.3 The asymptotic distribution of the      359 (5)
      test statistic
      23.4 The test                                364 (1)
      23.5 Weibull distribution                    364 (1)
      23.6 Loglogistic distribution                365 (1)
      23.7 Lognormal distribution                  366 (1)
      23.8 Bibliography                            367 (2)
  Chapter 24 Time-to-Failure of                    369 (14)
  Markov-Modulated Gamma Process with
  Application to Replacement Policies
          Christian Paroissin
          Landy Rabehasaina
      24.1 Introduction                            369 (1)
      24.2 Degradation model                       370 (1)
        24.2.1 Covariate process                   370 (1)
        24.2.2 Degradation process                 371 (1)
      24.3 Time-to-failure distribution            371 (5)
        24.3.1 Case of a non-modulated gamma       372 (1)
        process
        24.3.2 Case of a Markov-modulated gamma    373 (1)
        process
        24.3.3 Stochastic comparison               374 (2)
      24.4 Replacement policies                    376 (5)
        24.4.1 Block replacement policy            377 (2)
        24.4.2 Age replacement policy              379 (2)
      24.5 Conclusion                              381 (1)
      24.6 Acknowledgment                          381 (1)
      24.7 Bibliography                            382 (1)
  Chapter 25 Calculation of the Redundant          383 (8)
  Structure Reliability for Aging-type Elements
          Alexandr Antonov
          Alexandr Plyaskin
          Khizri Tataev
      25.1 Introduction                            383 (1)
      25.2 The operation process of the renewal    384 (2)
      and repaired products
      25.3 The model of the geometric process      386 (1)
      25.4 Task solution                           387 (2)
      25.5 Conclusion                              389 (1)
      25.6 Bibliography                            390 (1)
  Chapter 26 On Engineering Risks of Complex       391 (14)
  Hierarchical Systems Analysis
          Vladimir Rykov
      26.1 Introduction                            391 (1)
      26.2 Risk definition and measurement         392 (1)
      26.3 Engineering risk                        393 (2)
      26.4 Risk characteristics for general        395 (5)
      model calculation
        26.4.1 Lifelength and appropriate loss     395 (1)
        size CDF
        26.4.2 Probability of risk event           396 (1)
        evolution
        26.4.3 Lifelength and loss moments         397 (2)
        26.4.4 Mostly dangerous paths of risk      399 (1)
        event evolution and sensitivity analysis
      26.5 Risk analysis for short-time risk       400 (2)
      models
      26.6 Conclusion                              402 (1)
      26.7 Bibliography                            402 (3)
List of Authors                                    405 (4)
Index                                              409