Uniform Central Limit Theorems [Hardcover]

This expanded edition of the classic work on empirical processes now boasts several new proved theorems not in the first.This second edition of the classic work on empirical processes has been considerably expanded and revised. It now includes complete proofs of all results, including several new theorems not included in the first edition, such as Talagrand's generic chaining approach to boundedness of Gaussian processes and Gin? and Zinn's characterization of uniform Donsker classes.This second edition of the classic work on empirical processes has been considerably expanded and revised. It now includes complete proofs of all results, including several new theorems not included in the first edition, such as Talagrand's generic chaining approach to boundedness of Gaussian processes and Gin? and Zinn's characterization of uniform Donsker classes.This classic work on empirical processes has been considerably expanded and revised from the original edition. When samples become large, the probability laws of large numbers and central limit theorems are guaranteed to hold uniformly over wide domains. The author, an acknowledged expert, gives a thorough treatment of the subject, including the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Gin?-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. This new edition contains several proved theorems not included in the first edition, including the Bretagnolle-Massart theorem giving constants in the Komlos-Major-Tusnady rate of convergence for the classical empirical process, Massart's form of the Dvoretzky-Kiefer-Wolfowitz inequality with precise constant, Talagrand's generic chaining approach to boundedness of Gaussian processes, a characterization of uniform Glivenko-Cantell!