Weak Convergence and Empirical Processes: With Applications to Statistics (Hardcover)

Preface (vii)Reading Guide (ix)

Part I: Stochastic Convergence?1.1 Introduction: (1-6)?1.2 Outer Integrals and Measurable Majorants: (7-16)?1.3 Weak Convergence: (17 - 30)?1.4 Product Spaces: (31-35)?1.5 Spaces of Bounded Functions: (36 - 44)?1.6 Spaces of Locally Bounded Functions: (45 - 46)?1.7 The Ball Sigma-Field and Measurability of Suprema: (47 - 50)?1.8 Hilbert Spaces: (51 - 53)?1.9 Convergence: Almost surely and in probability: (54 - 58)?1.10 Convergence: Weak, Almost Uniform, and in Probabil- ity: (59 - 68)?1.11 Re_nements: (69 - 72)?1.12 Uniformity and Metrization: (73 - 76)?1.13 Skorokhod Space (new): (77 - 106)?1.14 Notes: (107 - 111)
Part 2: Empirical Processes: (113 - 370)?2.1 Introduction: (114 - 129)?2.2 Maximal Inequalities and Covering Numbers: (130 - 151)?2.3 Symmetrization and Measurability: (152 - 167)?2.4 Glivenko-Cantelli Theorems: (168 - 174)?2.5 Donsker Theorems: (175 - 181)?2.6 Uniform Entropy Numbers: (182 - 206)?2.7 Entropies of Function Classes (new title): (207 - 238)?2.8 Uniformity in the Underlying Distribution: (239 - 248)?2.9 Multiplier Central Limit Theorems: (249 - 262)?2.10 Permanence of the Glivenko-Cantelli and Donsker Prop- erties: (263 - 279)?2.11 The Central Limit Theorem for Processes: (280 - 299)?2.12 Partial Sum Processes: (300 - 306)?2.13 Other Donsker Classes: (307 - 312)?2.14 Maximal Inequalities and Tail Bounds: (313 - 348)?2.15 Concentration (new): (349 - 362)?2.16 Notes: (363 - 370)
Part 3: Statistical Applications: (371 - 558)?3.1 Introduction: (372 - 377)?3.2 M-Estimators: (378 - 403)?3.3 Z-Estimators: (404 - 415)?3.4 Rates of Convergence: (416 - 456)?3.5 Model Selection (new): (457 - 467)?3.6 Random Sample Size, Poissonization, and Kac Processes: (468 - 473)?3.7 Bootstrap: (474 - 488) 3.8 Two-Sample Problem: (489 - 495)?3.9 Independence Empirical Processes: (496 - 500)?3.10 Delta Method: (501 - 532)) 3.11 Contiguity: (533 - 543)?3.12 Convolution and Minimax Theorems: (544 - 554)?3.13 Random Empirical Processes: (555 - 572)?3.14 Notes: (573 - 579)?
Appendix: (581 - 623)?A.1 Inequalities: (582 - 589)?A.2 Gaussian Processes: (590 - 605)?A.3 Rademacher Processes: (606 - 607)?A.4 Isoperimetric Inequalities for Product Measures: (608 - 612))?A.5 Some Limit Theorems: (613 - 615)?A.6 More Inequalities: (616 - 621)?Notes: (622 - 623)
References (637)?Author Index (665)Subject Index (669)List of Symbols (676)