Format:
1 online resource (xiv, 436 pages)
ISBN:
9780521461023
,
9780521052214
,
9780511665622
Series Statement:
Cambridge studies in advanced mathematics 63
Content:
This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Giné-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. Other results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians working in probability, mathematical statisticians and computer scientists working in computer learning theory.
Content:
1. Introduction: Donsker's theorem, metric entropy, and inequalitites 2. Gaussian measures and processes 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis classes and Koltchinskii-Pollard entropy 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521461023
Additional Edition:
ISBN 9780521052214
Additional Edition:
Dudley, Richard M., 1938 - Uniform central limit theorems Cambridge [u.a.] : Cambridge University Press, 1999 ISBN 0521461022
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521461023
Language:
English
Subjects:
Mathematics
Keywords:
Zentraler Grenzwertsatz
DOI:
10.1017/CBO9780511665622
Author information:
Dudley, Richard M. 1938-
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