Normal approximation and asymptotic expansions [electronic resource]

• 作者： Bhattacharya, R. N. (Rabindra Nath), 1937-
• 其他作者：
  • Ranga Rao, R. (Ramaswamy), 1935-
• 其他題名：
  • Classics in applied mathematics
• 出版： Philadelphia : Society for Industrial and Applied Mathematics
• 叢書名： Classics in applied mathematics64
• 主題： Asymptotic expansions , Central limit theorem. , Convergence , Electronic books.
• ISBN： 9780898719895 (electronic bk.) 、 0898719895 (electronic bk.)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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. "Updated republication of the work first published by Robert E. Krieger Publishing Company, Inc., in 1986"--Copr. p.
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• 摘要註: 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.
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