{"product_id":"normal-approximation-and-asymptotic-expansions-paperback-softback-9780898718973","title":"Normal Approximation and Asymptotic Expansions (Paperback \/ softback) 9780898718973","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eNormal Approximation and Asymptotic Expansions\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA detailed treatment of various refinements of the multivariate central limit theorem.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eRabi N. Bhattacharya (Author), R. Ranga Rao (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780898718973\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 30 September 2010\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e338 pages\u003cbr\u003e24.6 x 17.3 x 1.7 cm, 0.481 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eAlthough Normal Approximation and Asymptotic Expansions 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 is also 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. With meticulous care, the authors develop the necessary background on: weak convergence theory, Fourier analysis, geometry of convex sets and the relationship between lattice random vectors and discrete subgroups of Rk.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface to the Classics Edition\u003cbr\u003e Preface\u003cbr\u003e 1. Weak convergence of probability measures and uniformity classes\u003cbr\u003e 2. Fourier transforms and expansions of characteristic functions\u003cbr\u003e 3. Bounds for errors of normal approximation\u003cbr\u003e 4. Asymptotic expansions-nonlattice distributions\u003cbr\u003e 5. Asymptotic expansions-lattice distributions\u003cbr\u003e 6. Two recent improvements\u003cbr\u003e 7. An application of Stein's method\u003cbr\u003e Appendix A.1. Random vectors and independence\u003cbr\u003e Appendix A.2. Functions of bounded variation and distribution functions\u003cbr\u003e Appendix A.3. Absolutely continuous, singular, and discrete probability measures\u003cbr\u003e Appendix A.4. The Euler–MacLaurin sum formula for functions of several variables\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Miscellaneous items [\u003ca title=\"See our other books on Miscellaneous items\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Miscellaneous%20items%20%5BWZ%5D%22\"\u003eWZ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"MP–SIA SIAM – Society for Industrial and Applied M","offers":[{"title":"Brand New","offer_id":52410752074008,"sku":"9780898718973","price":57.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780898718973i.jpg?v=1784251743","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/normal-approximation-and-asymptotic-expansions-paperback-softback-9780898718973","provider":"Freshly Printed Books","version":"1.0","type":"link"}