國立虎尾科技大學 |

Uniform central limit theorems /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Uniform central limit theorems // R.M. Dudley, Massachusetts Institute of Technology.
Author:	Dudley, R. M.
Description:	1 online resource (xii, 472 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Central limit theorem. -
Online resource:	https://doi.org/10.1017/CBO9781139014830
ISBN:	9781139014830 (ebook)

Uniform central limit theorems /
Dudley, R. M.

Uniform central limit theorems /R.M. Dudley, Massachusetts Institute of Technology. - Second edition. - 1 online resource (xii, 472 pages) :digital, PDF file(s). - Cambridge studies in advanced mathematics ;142. - Cambridge studies in advanced mathematics ;134..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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, 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.

ISBN: 9781139014830 (ebook)Subjects--Topical Terms:

782437
Central limit theorem.

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

Dewey Class. No.: 519.2

Uniform central limit theorems /
LDR:03026nam a2200325 i 4500 001 1122416
003 UkCbUP
005 20151005020622.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 240926s2014||||enk o ||1 0|eng|d
020 $a 9781139014830 (ebook)
020 $z 9780521498845 (hardback)
020 $z 9780521738415 (paperback)
035 $a CR9781139014830
040 $a UkCbUP $b eng $e rda $c UkCbUP
050 0 0 $a QA273.67 $b .D84 2014
082 0 0 $a 519.2 $2 23
100 1 $a Dudley, R. M. $3 685667
245 1 0 $a Uniform central limit theorems / $c R.M. Dudley, Massachusetts Institute of Technology.
250 $a Second edition.
264 1 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a 1 online resource (xii, 472 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
490 1 $a Cambridge studies in advanced mathematics ; $v 142
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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, 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.
650 0 $a Central limit theorem. $3 782437
776 0 8 $i Print version: $z 9780521498845
830 0 $a Cambridge studies in advanced mathematics ; $v 134. $3 1133579
856 4 0 $u https://doi.org/10.1017/CBO9781139014830