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Uniform central limit theorems /

Dudley, R. M.

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Uniform central limit theorems /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Uniform central limit theorems // R.M. Dudley.
作者:	Dudley, R. M.
出版者:	New York :Cambridge University Press, : 2014.,
面頁冊數:	xii, 472 p. :ill ;23 cm.
標題:	Central limit theorem. -
ISBN:	9780521738415

Uniform central limit theorems /
Dudley, R. M.

Uniform central limit theorems /R.M. Dudley. - 2nd ed. - New York :Cambridge University Press,2014. - xii, 472 p. :ill ;23 cm. - Cambridge studies in advanced mathematics ;142.

Includes bibliographical references and indexes.

Donsker's theorem and inequalities --

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, Gine; 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.

ISBN: 9780521738415US50.00

LCCN: 2013011303Subjects--Topical Terms:

648367
Central limit theorem.

LC Class. No.: QA273.67 / .D84 2014

Dewey Class. No.: 519.2

Uniform central limit theorems /
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020 $a 9780521738415 $q (pbk.) : $c US50.00
020 $a 0521738415 $q (pbk.)
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050 0 0 $a QA273.67 $b .D84 2014
082 0 0 $a 519.2 $2 23
100 1 $a Dudley, R. M. $3 1245266
245 1 0 $a Uniform central limit theorems / $c R.M. Dudley.
250 $a 2nd ed.
260 # $a New York : $b Cambridge University Press, $c 2014.
300 $a xii, 472 p. : $b ill ; $c 23 cm.
490 1 0 $a Cambridge studies in advanced mathematics ; $v 142
504 $a Includes bibliographical references and indexes.
505 0 # $t Donsker's theorem and inequalities -- $t Gaussian processes : sample continuity -- $t Definition of Donsker classes -- $t Vapnik-Cervonenkis combinatorics -- $t Measurability -- $t Limit theorems for VC-type classes -- $t Metric entropy with bracketing -- $t Approximation of functions and sets -- $t Two samples and the bootstrap -- $t Uniform and universal limit theorems -- $t Classes too large to be Donsker -- $t Differentiating under an integral sign -- $t Multinomial distributions -- $t Measures on nonseparable metric spaces -- $t An extension of Lusin's theorem -- $t Bochner and Pettis integrals -- $t Non-existence of some linear forms -- $t Separation of analytic sets -- $t Young-Orlicz spaces -- $t Versions of isonormal processes.
520 # $a 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, Gine; 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.
650 # 0 $a Central limit theorem. $3 648367