東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Weak convergence and empirical proce...

Vaart, A. W. van der.

Linked to FindBook

Google Book

Amazon

博客來

Weak convergence and empirical processes = with applications to statistics /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Weak convergence and empirical processes/ by A. W. van der Vaart, Jon A. Wellner.
Reminder of title:	with applications to statistics /
Author:	Vaart, A. W. van der.
other author:	Wellner, Jon A.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xvii, 679 p. :ill., digital ;24 cm.
[NT 15003449]:	Preface -- Reading Guide -- Part I: Stochastic Convergence -- Part 2: Empirical Processes -- Part 3: Statistical Applications -- Appendix -- References -- Author Index -- Subject Index -- List of Symbols.
Contained By:	Springer Nature eBook
Subject:	Stochastic processes. -
Online resource:	https://doi.org/10.1007/978-3-031-29040-4
ISBN:	9783031290404

Weak convergence and empirical processes = with applications to statistics /
Vaart, A. W. van der.

Weak convergence and empirical processeswith applications to statistics /[electronic resource] :by A. W. van der Vaart, Jon A. Wellner. - Second edition. - Cham :Springer International Publishing :2023. - xvii, 679 p. :ill., digital ;24 cm. - Springer series in statistics,2197-568X. - Springer series in statistics..

Preface -- Reading Guide -- Part I: Stochastic Convergence -- Part 2: Empirical Processes -- Part 3: Statistical Applications -- Appendix -- References -- Author Index -- Subject Index -- List of Symbols.

This book provides an account of weak convergence theory, empirical processes, and their application to a wide variety of problems in statistics. The first part of the book presents a thorough treatment of stochastic convergence in its various forms. Part 2 brings together the theory of empirical processes in a form accessible to statisticians and probabilists. In Part 3, the authors cover a range of applications in statistics including rates of convergence of estimators; limit theorems for M- and Z-estimators; the bootstrap; the functional delta-method and semiparametric estimation. Most of the chapters conclude with "problems and complements." Some of these are exercises to help the reader's understanding of the material, whereas others are intended to supplement the text. This second edition includes many of the new developments in the field since publication of the first edition in 1996: Glivenko-Cantelli preservation theorems; new bounds on expectations of suprema of empirical processes; new bounds on covering numbers for various function classes; generic chaining; definitive versions of concentration bounds; and new applications in statistics including penalized M-estimation, the lasso, classification, and support vector machines. The approximately 200 additional pages also round out classical subjects, including chapters on weak convergence in Skorokhod space, on stable convergence, and on processes based on pseudo-observations.

ISBN: 9783031290404

Standard No.: 10.1007/978-3-031-29040-4doiSubjects--Topical Terms:

520663
Stochastic processes.

LC Class. No.: QA274

Dewey Class. No.: 519.2

Weak convergence and empirical processes = with applications to statistics /
LDR:02763nmm a2200349 a 4500 001 2333208
003 DE-He213
005 20230711192053.0
006 m d
007 cr nn 008maaau
008 240402s2023 sz s 0 eng d
020 $a 9783031290404 $q (electronic bk.)
020 $a 9783031290381 $q (paper)
024 7 $a 10.1007/978-3-031-29040-4 $2 doi
035 $a 978-3-031-29040-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
082 0 4 $a 519.2 $2 23
090 $a QA274 $b .V217 2023
100 1 $a Vaart, A. W. van der. $3 686654
245 1 0 $a Weak convergence and empirical processes $h [electronic resource] : $b with applications to statistics / $c by A. W. van der Vaart, Jon A. Wellner.
250 $a Second edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xvii, 679 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer series in statistics, $x 2197-568X
505 0 $a Preface -- Reading Guide -- Part I: Stochastic Convergence -- Part 2: Empirical Processes -- Part 3: Statistical Applications -- Appendix -- References -- Author Index -- Subject Index -- List of Symbols.
520 $a This book provides an account of weak convergence theory, empirical processes, and their application to a wide variety of problems in statistics. The first part of the book presents a thorough treatment of stochastic convergence in its various forms. Part 2 brings together the theory of empirical processes in a form accessible to statisticians and probabilists. In Part 3, the authors cover a range of applications in statistics including rates of convergence of estimators; limit theorems for M- and Z-estimators; the bootstrap; the functional delta-method and semiparametric estimation. Most of the chapters conclude with "problems and complements." Some of these are exercises to help the reader's understanding of the material, whereas others are intended to supplement the text. This second edition includes many of the new developments in the field since publication of the first edition in 1996: Glivenko-Cantelli preservation theorems; new bounds on expectations of suprema of empirical processes; new bounds on covering numbers for various function classes; generic chaining; definitive versions of concentration bounds; and new applications in statistics including penalized M-estimation, the lasso, classification, and support vector machines. The approximately 200 additional pages also round out classical subjects, including chapters on weak convergence in Skorokhod space, on stable convergence, and on processes based on pseudo-observations.
650 0 $a Stochastic processes. $3 520663
650 0 $a Convergence. $3 589031
650 0 $a Distribution (Probability theory) $3 533179
650 0 $a Sampling (Statistics) $3 545623
650 1 4 $a Applied Statistics. $3 3300946
650 2 4 $a Statistical Theory and Methods. $3 891074
650 2 4 $a Bayesian Inference. $3 3386929
700 1 $a Wellner, Jon A. $3 3663787
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Springer series in statistics. $3 1315057
856 4 0 $u https://doi.org/10.1007/978-3-031-29040-4
950 $a Mathematics and Statistics (SpringerNature-11649)