Uniform central limit theorems
 Author/Creator
 Dudley, R. M. (Richard M.)
 Language
 English.
 Edition
 Second edition.
 Publication
 New York : Cambridge University Press, 2014.
 Physical description
 xii, 472 pages ; 23 cm.
 Series
 Cambridge studies in advanced mathematics ; 142.
Access
Available online

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QA273.67 .D84 2014

Unknown
QA273.67 .D84 2014
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Contents/Summary
 Bibliography
 Includes bibliographical references (pages 449461) and index.
 Contents

 1. Donsker's theorem and inequalities 2. Gaussian processes, sample continuity 3. Definition of Donsker classes 4. VapnikCervonenkis combinatorics 5. Measurability 6. Limit theorems for VCtype classes 7. Metric entropy with bracketing 8. Approximation of functions and sets 9. Two samples and the bootstrap 10. Uniform and universal limit theorems 11. Classes too large to be Donsker Appendix A. Differentiating under an integral sign Appendix B. Multinomial distributions Appendix C. Measures on nonseparable metric spaces Appendix D. An extension of Lusin's theorem Appendix E. Bochner and Pettis integrals Appendix F. Nonexistence of some linear forms Appendix G. Separation of analytic sets Appendix H. YoungOrlicz spaces Appendix I. Versions of isonormal processes.
 (source: Nielsen Book Data)
 Publisher's Summary
 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, Gine 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 infinitedimensional 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.
(source: Nielsen Book Data)  Supplemental links
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Subjects
 Subject
 Central limit theorem.
Bibliographic information
 Publication date
 2014
 Responsibility
 R.M. Dudley, Massachusetts Institute of Technology.
 Series
 Cambridge studies in advanced mathematics ; 142
 ISBN
 9780521498845 (hardback)
 0521498848 (hardback)
 9780521738415 (paperback)
 0521738415 (paperback)