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Uniform central limit theorems

Dudley, R. M.

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Uniform central limit theorems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Uniform central limit theorems/ R.M. Dudley.
作者:	Dudley, R. M.
出版者:	Cambridge :Cambridge University Press, : 1999.,
面頁冊數:	xiv, 436 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	1. Introduction: Donsker's theorem, metric entropy, and inequalitites 2. Gaussian measures and processes 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis classes and Koltchinskii-Pollard entropy 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems.
標題:	Central limit theorem. -
電子資源:	https://doi.org/10.1017/CBO9780511665622
ISBN:	9780511665622

Uniform central limit theorems
Dudley, R. M.

Uniform central limit theorems[electronic resource] /R.M. Dudley. - Cambridge :Cambridge University Press,1999. - xiv, 436 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;63. - Cambridge studies in advanced mathematics ;63..

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

1. Introduction: Donsker's theorem, metric entropy, and inequalitites 2. Gaussian measures and processes 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis classes and Koltchinskii-Pollard entropy 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems.

This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Gine-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. Other results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians working in probability, mathematical statisticians and computer scientists working in computer learning theory.

ISBN: 9780511665622Subjects--Topical Terms:

648367
Central limit theorem.

LC Class. No.: QA273.67 / .D84 1999

Dewey Class. No.: 519.2

Uniform central limit theorems
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 1. Introduction: Donsker's theorem, metric entropy, and inequalitites 2. Gaussian measures and processes 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis classes and Koltchinskii-Pollard entropy 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems.
520 $a This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment of Vapnik-Chervonenkis combinatorics, the Ossiander L2 bracketing central limit theorem, the Gine-Zinn bootstrap central limit theorem in probability, the Bronstein theorem on approximation of convex sets, and the Shor theorem on rates of convergence over lower layers. Other results of Talagrand and others are surveyed without proofs in separate sections. Problems are included at the end of each chapter so the book can be used as an advanced text. The book will interest mathematicians working in probability, mathematical statisticians and computer scientists working in computer learning theory.
650 0 $a Central limit theorem. $3 648367
830 0 $a Cambridge studies in advanced mathematics ; $v 63. $3 3470695
856 4 0 $u https://doi.org/10.1017/CBO9780511665622