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Normal approximation and asymptotic ...

Bhattacharya, R. N. (1937-)

Normal approximation and asymptotic expansions

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Normal approximation and asymptotic expansionsRabi N. Bhattacharya, R. Ranga Rao.
作者:	Bhattacharya, R. N.
其他作者:	Ranga Rao, R.
出版者:	Philadelphia :Society for Industrial and Applied Mathematics,c2010.
面頁冊數:	1 electronic text (xxii, 316 p.)
附註:	"Updated republication of the work first published by Robert E. Krieger Publishing Company, Inc., in 1986"--Copr. p.
標題:	Asymptotic expansions.
電子資源:	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 ;vol. 2..

"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:

215351
Asymptotic expansions.
Index Terms--Genre/Form:

214472
Electronic books.

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

Dewey Class. No.: 519.2

Normal approximation and asymptotic expansions
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300 $a 1 electronic text (xxii, 316 p.)
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 215351
650 0 $a Central limit theorem. $3 183299
650 0 $a Convergence. $3 182684
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830 0 $a Classics in applied mathematics ; $v vol. 2. $3 436573
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