[下载]Introduction to Empirical and semiparametric models - Michael R. Kosorok

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【书名】 Introduction to Empirical and semiparametric models
【作者】Michael R. Kosorok
【出版社】Springer
【版本】第一版
【出版日期】January 31, 2008
【文件格式】PDF
【文件大小】4.08MB
【页数】483 pages
【ISBN出版号】978-0387749778
【资料类别】统计学
【市面定价】N/A
【扫描版还是影印版】 清晰版
【是否缺页】无
【关键词】 Empirical process, Semiparametric, Bootstrap, M-Estimation, The Functional Delta Methodes
【内容简介】Springer Series in Statistics 的一本新书，网站上还没有完全版。这本书非常适合高年级本科生和研究生深入学习empirical process 和semiparametric models。本书一大特色就是例子很多，使得最新的理论生动起来。

 

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[下载]Introduction to Empirical and semiparametric models - Michael R. Kosorok
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【目录】
Preface vii
IOverview 1
1 Introduction 3
2 An Overview of Empirical Processes 9
2.1 TheMainFeatures....................... 9
2.2 EmpiricalProcessTechniques................. 13
2.2.1 StochasticConvergence ................ 13
2.2.2 Entropy for Glivenko-Cantelli and Donsker Theorems 16
2.2.3 Bootstrapping Empirical Processes . . . . . . . . . . 19
2.2.4 The Functional Delta Method . . . . . . . . . . . . . 21
2.2.5 Z-Estimators ...................... 24
2.2.6 M-Estimators...................... 28
2.3 OtherTopics .......................... 30
2.4 Exercises ............................ 32
2.5 Notes .............................. 33
3 Overview of Semiparametric Inference 35
3.1 SemiparametricModelsandEfficiency ............ 35
3.2 Score Functions and Estimating Equations . . . . . . . . . . 39
3.3 MaximumLikelihoodEstimation ............... 44
xContents
3.4 OtherTopics .......................... 47
3.5 Exercises ............................ 48
3.6 Notes .............................. 48
4 Case Studies I 49
4.1 LinearRegression........................ 50
4.1.1 MeanZeroResiduals.................. 50
4.1.2 MedianZeroResiduals................. 52
4.2 CountingProcessRegression ................. 54
4.2.1 TheGeneralCase ................... 55
4.2.2 TheCoxModel..................... 59
4.3 TheKaplan-MeierEstimator ................. 60
4.4 Efficient Estimating Equations for Regression . . . . . . . . 62
4.4.1 Simple Linear Regression . . . . . . . . . . . . . . . 66
4.4.2 A Poisson Mixture Regression Model . . . . . . . . . 69
4.5 Partly Linear Logistic Regression . . . . . . . . . . . . . . . 69
4.6 Exercises ............................ 72
4.7 Notes .............................. 72
II Empirical Processes 75
5 Introduction to Empirical Processes 77
6 Preliminaries for Empirical Processes 81
6.1 MetricSpaces.......................... 81
6.2 OuterExpectation ....................... 88
6.3 Linear Operators and Functional Differentiation . . . . . . . 93
6.4 Proofs .............................. 96
6.5 Exercises ............................ 100
6.6 Notes .............................. 102
7 Stochastic Convergence 103
7.1 StochasticProcessesinMetricSpaces ............ 103
7.2 WeakConvergence ....................... 107
7.2.1 GeneralTheory..................... 107
7.2.2 Spaces of Bounded Functions . . . . . . . . . . . . . 113
7.3 OtherModesofConvergence ................. 115
7.4 Proofs .............................. 120
7.5 Exercises ............................ 125
7.6 Notes .............................. 126
8 Empirical Process Methods 127
8.1 MaximalInequalities...................... 128
8.1.1 Orlicz Norms and Maxima . . . . . . . . . . . . . . . 128
8.1.2 Maximal Inequalities for Processes . . . . . . . . . . 131
8.2 The Symmetrization Inequality and Measurability . . . . . 138
8.3 Glivenko-CantelliResults ................... 144
8.4 DonskerResults......................... 148
8.5 Exercises ............................ 151
8.6 Notes .............................. 153
9 Entropy Calculations 155
9.1 UniformEntropy........................ 156
9.1.1 VC-Classes ....................... 156
9.1.2 BUEIClasses...................... 162
9.2 BracketingEntropy....................... 166
9.3 Glivenko-CantelliPreservation ................ 169
9.4 DonskerPreservation...................... 172
9.5 Proofs .............................. 173
9.6 Exercises ............................ 176
9.7 Notes .............................. 178
10 Bootstrapping Empirical Processes 179
10.1 The Bootstrap for Donsker Classes . . . . . . . . . . . . . . 180
10.1.1 An Unconditional Multiplier Central Limit Theorem 181
10.1.2 Conditional Multiplier Central Limit Theorems . . . 183
10.1.3 Bootstrap Central Limit Theorems . . . . . . . . . . 187
10.1.4 Continuous Mapping Results . . . . . . . . . . . . . 189
10.2 The Bootstrap for Glivenko-Cantelli Classes . . . . . . . . . 193
10.3ASimpleZ-EstimatorMasterTheorem ........... 196
10.4Proofs .............................. 198
10.5Exercises ............................ 204
10.6Notes .............................. 205
11 Additional Empirical Process Results 207
11.1 Bounding Moments and Tail Probabilities . . . . . . . . . . 208
11.2SequencesofFunctions..................... 211
11.3 Contiguous Alternatives . . . . . . . . . . . . . . . . . . . . 214
11.4 Sums of Independent but not Identically Distributed Stochas-
ticProcesses .......................... 218
11.4.1CentralLimitTheorems................ 218
11.4.2BootstrapResults ................... 222
11.5 Function Classes Changing with n .............. 224
11.6DependentObservations.................... 227
11.7Proofs .............................. 230
11.8Exercises ............................ 233
11.9Notes .............................. 233
12 The Functional Delta Method 235
12.1MainResultsandProofs.................... 235
12.2Examples ............................ 237
12.2.1Composition ...................... 237
12.2.2 Integration ....................... 238
12.2.3ProductIntegration .................. 242
12.2.4 Inversion ........................ 246
12.2.5OtherMappings .................... 249
12.3Exercises ............................ 249
12.4Notes .............................. 250
13 Z-Estimators 251
13.1Consistency........................... 252
13.2WeakConvergence ....................... 253
13.2.1TheGeneralSetting .................. 254
13.2.2UsingDonskerClasses................. 254
13.2.3 A Master Theorem and the Bootstrap . . . . . . . . 255
13.3UsingtheDeltaMethod.................... 258
13.4Exercises ............................ 262
13.5Notes .............................. 262
14 M-Estimators 263
14.1TheArgmaxTheorem..................... 264
14.2Consistency........................... 266
14.3RateofConvergence ...................... 267
14.4 Regular Euclidean M-Estimators . . . . . . . . . . . . . . . 270
14.5Non-RegularExamples..................... 271
14.5.1AChange-PointModel................. 271
14.5.2 Monotone Density Estimation . . . . . . . . . . . . . 277
14.6Exercises ............................ 280
14.7Notes .............................. 282
15 Case Studies II 283
15.1 Partly Linear Logistic Regression Revisited . . . . . . . . . 283
15.2TheTwo-ParameterCoxScoreProcess............ 287
15.3 The Proportional Odds Model Under Right Censoring . . . 291
15.3.1 Nonparametric Maximum Likelihood Estimation . . 292
15.3.2Existence ........................ 293
15.3.3Consistency....................... 295
15.3.4 Score and Information Operators . . . . . . . . . . . 297
15.3.5 Weak Convergence and Bootstrap Validity . . . . . . 301
15.4TestingforaChange-point .................. 303
15.5 Large p Small n Asymptotics for Microarrays . . . . . . . . 306
15.5.1 Assessing P-Value Approximations . . . . . . . . . . 308
15.5.2 Consistency of Marginal Empirical Distribution
Functions ........................ 309
15.5.3 Inference for Marginal Sample Means . . . . . . . . 312
15.6Exercises ............................ 314
15.7Notes .............................. 315
III Semiparametric Inference 317
16 Introduction to Semiparametric Inference 319
17 Preliminaries for Semiparametric Inference 323
17.1Projections ........................... 323
17.2HilbertSpaces ......................... 324
17.3MoreonBanachSpaces .................... 328
17.4Exercises ............................ 332
17.5Notes .............................. 332
18 Semiparametric Models and Efficiency 333
18.1TangentSetsandRegularity.................. 333
18.2Efficiency ............................ 337
18.3OptimalityofTests....................... 342
18.4Proofs .............................. 345
18.5Exercises ............................ 346
18.6Notes .............................. 347
19 Efficient Inference for Finite-Dimensional Parameters 349
19.1EfficientScoreEquations ................... 350
19.2 Profile Likelihood and Least-Favorable Submodels . . . . . 351
19.2.1 The Cox Model for Right Censored Data . . . . . . 352
19.2.2 The Proportional Odds Model for Right
CensoredData ..................... 353
19.2.3 The Cox Model for Current Status Data . . . . . . . 355
19.2.4 Partly Linear Logistic Regression . . . . . . . . . . . 356
19.3Inference............................. 357
19.3.1 Quadratic Expansion of the Profile Likelihood . . . . 357
19.3.2TheProfileSampler .................. 363
19.3.3ThePenalizedProfileSampler ............ 369
19.3.4OtherMethods..................... 371
19.4Proofs .............................. 373
19.5Exercises ............................ 376
19.6Notes .............................. 377
20 Efficient Inference for Infinite-Dimensional Parameters 379
20.1 Semiparametric Maximum Likelihood Estimation . . . . . . 379
20.2Inference............................. 387
20.2.1 Weighted and Nonparametric Bootstraps . . . . . . 387
20.2.2 The Piggyback Bootstrap . . . . . . . . . . . . . . . 389
20.2.3OtherMethods..................... 393
20.3Exercises ............................ 395
20.4Notes .............................. 395
21 Semiparametric M-Estimation 397
21.1 Semiparametric M-estimators . . . . . . . . . . . . . . . . . 399
21.1.1MotivatingExamples.................. 399
21.1.2 General Scheme for Semiparametric M-Estimators . 401
21.1.3 Consistency and Rate of Convergence . . . . . . . . 402
21.1.4
√n Consistency and Asymptotic Normality . . . . . 402
21.2 Weighted M-Estimators and the Weighted Bootstrap . . . . 407
21.3EntropyControl ........................ 410
21.4ExamplesContinued...................... 412
21.4.1 Cox Model with Current Status Data
(Example1,Continued)................ 412
21.4.2 Binary Regression Under Misspecified Link
Function(Example2,Continued)........... 415
21.4.3 Mixture Models (Example 3, Continued) . . . . . . . 418
21.5PenalizedM-estimation .................... 420
21.5.1 Binary Regression Under Misspecified Link
Function(Example2,Continued)........... 420
21.5.2TwoOtherExamples ................. 422
21.6Exercises ............................ 423
21.7Notes .............................. 423
22 Case Studies III 425
22.1 The Proportional Odds Model Under Right Censoring
Revisited ............................ 426
22.2 Efficient Linear Regression . . . . . . . . . . . . . . . . . . . 430
22.3TemporalProcessRegression ................. 436
22.4 A Partly Linear Model for Repeated Measures . . . . . . . 444
22.5Proofs .............................. 453
22.6Exercises ............................ 456
22.7Notes .............................. 457
References 459
Author Index 470
List of symbols 473
Subject Index 477

【整理书评】

"Generally, this is a great book on empirical processes and semiparametric methods. It should be on the must-read list for a serious statistician, biostatistician, or econometrician." (Biometrics, September 2008)

"Introduction to Empirical Processes and Semiparametric Inference is a very good combination of both the empirical processes and semiparametric theories. This is the first book of its kind....I agree with the author that this book is 'more of a textbook than a research monograph.' As the semiparametric inference is currently an extremely active research area in statistical research, the book will open the door for graduate students to identify significant future research potentials. In fact, this book contains the author's newest research result, the application of semiparametric method in microarray data analysis. This book can be used as a textbook for graduate students in statistics, biostatistics, and economics (econometrics). In fact, the contents of this book can be tailored for different courses."

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关键词：introduction troduction Parametric Empirical semipara models Michael Empirical introduction Kosorok

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