Uniform Central Limit Theorems (Cambridge Studies in Advanced Mathematics)

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9780521738415: Uniform Central Limit Theorems (Cambridge Studies in Advanced Mathematics)

This second edition of a classic work has been considerably expanded and revised, now with 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 Giné and Zinn's characterization of uniform Donsker classes.

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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 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–Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes, and the Bousquet–Koltchinskii–Panchenko 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.

Biografía del autor:

R. M. Dudley is a Professor of Mathematics at the Massachusetts Institute of Technology in Cambridge, Massachusetts.

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Richard M. Dudley
Verlag: Cambridge University Press Mai 2014 (2014)
ISBN 10: 0521738415 ISBN 13: 9780521738415
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Buchbeschreibung Cambridge University Press Mai 2014, 2014. Taschenbuch. Buchzustand: Neu. 227x153x25 mm. Neuware - 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. 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-Cantelli classes of functions, Giné and Zinn's characterization of uniform Donsker classes (i.e., classing Donsker uniformly over all probability measures P), and the Bousquet-Koltchinskii-Panchenko 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. 424 pp. Englisch. Artikel-Nr. 9780521738415

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