Manual Normal Approximation and Asymptotic Expansions (Clasics in Applied Mathmatics)

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Description Although Normal Approximation and Asymptotic Expansions was first published in , 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.

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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. Other books in this series. Add to basket. Table of contents Preface to the Classics Edition; Preface; 1.

Rabi N. Bhattacharya | bodcidelijphae.ml

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.

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Asymptotic expansions-lattice distributions; 6. Two recent improvements; 7. An application of Stein's method; Appendix A. Random vectors and independence; Appendix A.

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Functions of bounded variation and distribution functions; Appendix A. Absolutely continuous, singular, and discrete probability measures; Appendix A.

About Rabi N. Bhattacharya Rabi N.

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    ISBN 13: 9780898718973

    Access provided by: anon Sign Out. Asymptotic expansions of the solutions of nonlinear evolution equations Abstract: A lot of methods have been developed for finding approximate periodic solutions of nonlinear equations on the basis of classic perturbation theory. All of them are developed under assuming the nonlinearity to be weak that allows us to separate all of the motions onto fast and slow ones. However the majority of those methods are limited by the first level solutions because of either principal difficulties the method of averaging or technical causes connected with the awkward calculations and absence of regular algorithm.

    Such algorithm is developed in the present work as well as its program realization is carried out.

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    Besides that the weak nonlinearity was shown not to be the necessary condition for separating motions onto fast and slow. It is quite enough to redetermine the parameter of expansion into series within the frame of used spectral method.