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Uniform central limit theorems

Dudley, R. M.

Uniform central limit theorems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Uniform central limit theoremsR.M. Dudley.
作者:	Dudley, R. M.
出版者:	Cambridge :Cambridge University Press,2014.
面頁冊數:	xii, 472 p. :ill., digital ;24 cm.
標題:	Central limit theorem.
電子資源:	https://doi.org/10.1017/CBO9781139014830
ISBN:	9781139014830$q(electronic bk.)

Uniform central limit theorems
Dudley, R. M.

Uniform central limit theorems[electronic resource] /R.M. Dudley. - 2nd ed. - Cambridge :Cambridge University Press,2014. - xii, 472 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;142. - Cambridge studies in advanced mathematics ;105..

Machine generated contents note: 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, Gine 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.

ISBN: 9781139014830$q(electronic bk.)Subjects--Topical Terms:

183299
Central limit theorem.

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

Dewey Class. No.: 519.2

Uniform central limit theorems
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245 1 0 $a Uniform central limit theorems $h [electronic resource] / $c R.M. Dudley.
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300 $a xii, 472 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 142
505 8 $a Machine generated contents note: 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.
520 $a 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, Gine 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.
650 0 $a Central limit theorem. $3 183299
830 0 $a Cambridge studies in advanced mathematics ; $v 105. $3 541725
856 4 0 $u https://doi.org/10.1017/CBO9781139014830