Uniform Central Limit Theorems

In this new edition of a classic work on empirical processes the author an acknowledged expert gives a thorough treatment of the subject with the addition of several proved theorems not included in the first edition including the BretagnolleMassart theorem giving constants in the KomlosMajorTusnady rate of convergence for the classical empirical process Massart''s form of the DvoretzkyKieferWolfowitz inequality with precise constant Talagrand''s generic chaining approach to boundedness of Gaussian processes a characterization of uniform GlivenkoCantelli classes of functions Gin and Zinn''s characterization of uniform Donsker classes and the BousquetKoltchinskiiPanchenko theorem that the convex hull of a uniform Donsker class is uniform Donsker. The book will be an essential reference for mathematicians working in infinite-dimensional central limit theorems mathematical statisticians and computer scientists working in computer learning theory. Problems are included at the end of each chapter so the book can also be used as an advanced text.