Uniform Central Limit Theorems

R. m. dudley (author)

482 pages, parution le 23/02/2014

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Résumé

R. M. Dudley is a Professor of Mathematics at the Massachusetts Institute of Technology in Cambridge, Massachusetts.Previous edition: 1999.1. Donsker's theorem and inequalities; 2. Gaussian processes, sample continuity; 3. Definition of Donsker classes; 4. Vapnik-Cervonenkis combinatorics; 5. Measurability; 6. Limit theorems for VC-type 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. Non-existence of some linear forms; Appendix G. Separation of analytic sets; Appendix H. Young-Orlicz spaces; Appendix I. Versions of isonormal processes.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.2nd editionQA273.67Central limit theorem.1EnglandCambridgeR.M. Dudley.Cambridge Studies in Advanced Mathematics142

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	R. m. dudley (author)
Parution	23/02/2014
Nb. de pages	482
Format	152 x 228
Poids	640g
EAN13	9780521738415

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Uniform Central Limit Theorems

Résumé

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