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Normal approximation and asymptotic expansions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Normal approximation and asymptotic expansions/ Rabi N. Bhattacharya, R. Ranga Rao.
Author:	Bhattacharya, R. N.
other author:	Ranga Rao, R.
Published:	Philadelphia :Society for Industrial and Applied Mathematics, : c2010.,
Description:	1 electronic text (xxii, 316 p.)
Notes:	"Updated republication of the work first published by Robert E. Krieger Publishing Company, Inc., in 1986"--Copr. p.
Subject:	Asymptotic expansions. -
Online resource:	http://portal.igpublish.com/iglibrary/search/SIAMB0000414.html
ISBN:	9780898719895 (electronic bk.)

Normal approximation and asymptotic expansions
Bhattacharya, R. N.1937-

Normal approximation and asymptotic expansions[electronic resource] /Rabi N. Bhattacharya, R. Ranga Rao. - Philadelphia :Society for Industrial and Applied Mathematics,c2010. - 1 electronic text (xxii, 316 p.) - Classics in applied mathematics ;64. - Classics in applied mathematics ;63..

"Updated republication of the work first published by Robert E. Krieger Publishing Company, Inc., in 1986"--Copr. p.

Includes bibliographical references and index.

Preface to the classics edition -- Preface -- 1. Weak convergence of probability measures and uniformity classes -- 2. Fourier transforms and expansions of characteristic functions -- 3. Bounds for errors of normal approximation -- 4. Asymptotic expansions, nonlattice distributions -- 5. Asymptotic expansions, lattice distributions -- 6. Two recent improvements -- 7. An application of Stein's method -- Appendix A.1. Random vectors and independence -- Appendix A.2. Functions of bounded variation and distribution functions -- Appendix A.3. Absolutely continuous, singular, and discrete probability measures -- Appendix A.4. The Euler-MacLaurin sum formula for functions of several variables -- References -- Index.

Although this was first published in 1976, it has gained new significance and renewed interest among statisticians due to the developments of modern statistical techniques such as the bootstrap, the efficacy of which can be ascertained by asymptotic expansions. This also is the only book containing a detailed treatment of various refinements of the multivariate central limit theorem (CLT), including Berry-Essen-type error bounds for probabilities of general classes of functions and sets, and asymptotic expansions for both lattice and non-lattice distributions.

ISBN: 9780898719895 (electronic bk.)Subjects--Topical Terms:

196999
Asymptotic expansions.
Index Terms--Genre/Form:

96803
Electronic books.

LC Class. No.: QA273.67 / .B48 2010eb

Dewey Class. No.: 519.2

Normal approximation and asymptotic expansions
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490 1 $a Classics in applied mathematics ; $v 64
500 $a "Updated republication of the work first published by Robert E. Krieger Publishing Company, Inc., in 1986"--Copr. p.
504 $a Includes bibliographical references and index.
505 0 $a Preface to the classics edition -- Preface -- 1. Weak convergence of probability measures and uniformity classes -- 2. Fourier transforms and expansions of characteristic functions -- 3. Bounds for errors of normal approximation -- 4. Asymptotic expansions, nonlattice distributions -- 5. Asymptotic expansions, lattice distributions -- 6. Two recent improvements -- 7. An application of Stein's method -- Appendix A.1. Random vectors and independence -- Appendix A.2. Functions of bounded variation and distribution functions -- Appendix A.3. Absolutely continuous, singular, and discrete probability measures -- Appendix A.4. The Euler-MacLaurin sum formula for functions of several variables -- References -- Index.
520 3 $a Although this was first published in 1976, it has gained new significance and renewed interest among statisticians due to the developments of modern statistical techniques such as the bootstrap, the efficacy of which can be ascertained by asymptotic expansions. This also is the only book containing a detailed treatment of various refinements of the multivariate central limit theorem (CLT), including Berry-Essen-type error bounds for probabilities of general classes of functions and sets, and asymptotic expansions for both lattice and non-lattice distributions.
588 $a Description based on print version record.
650 0 $a Asymptotic expansions. $3 196999
650 0 $a Central limit theorem. $3 258921
650 0 $a Convergence. $3 258922
655 0 $a Electronic books. $2 local. $3 96803
700 1 $a Ranga Rao, R. $q (Ramaswamy), $d 1935- $3 258920
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830 0 $a Classics in applied mathematics ; $v 63. $3 258914
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