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

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

 Machine generated contents note: 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.
 Summary
 "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 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 (i.e., classing Donsker uniformly over all probability measures P), 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" Provided by publisher.
 Supplemental links
 Cover image
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
 0521498848
 9780521738415
 0521738415