Springer Series in Statistics / Weak Convergence and Empirical Processes

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 -

A.W. van der Vaart is a Professor of Statistics at Delft University, the Netherlands. He earned his Ph.D. in Mathematics from Leiden University. His research interests are in statistics and probability, as mathematical disciplines and in their applications to other sciences, with an emphasis on statistical models with large parameter spaces. He is a member of the Royal Netherlands Academy of Arts and Sciences and recipient of the Spinoza prize. He is a former president of the Netherlands Society for Statistics and Operations Research and served the national and international mathematical and statistical communities in various capacities. He has authored or co-authored eight books, one awarded with the DeGroot prize.

Jon A. Wellner is a Professor of Statistics at the University of Washington, Seattle. He earned his Ph.D. in Statistics from the University of Washington. His research interests include uses of large sample theory in statistics, theory of empirical processes and probability in high-dimensional settings, and efficient estimation for semiparametric models. He is also interested in statistical methods under shape constraints. He is a member of the American Association for the Advancement of Science, the Institute of Mathematical Statistics, the Bernoulli Society, and the International Statistical Institute, as well as the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the American Mathematical Society. He is a past President of the Institute of Mathematical Statistics, has served as an editor or co-editor of the Annals of Statistics and Statistical Science, and has co-authored or co-edited ten books.