Normal Approximation and Asymptotic Expansions
Normal Approximation and Asymptotic Expansions

Author: Rabindra Nath Bhattacharya

Publisher:

Published: 1986

Total Pages: 316

ISBN-13: 9780898719895

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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.

Normal Approximation and Asymptotic Expansions
Normal Approximation and Asymptotic Expansions

Author: Rabi N. Bhattacharya

Publisher: John Wiley & Sons

Published: 1976-04-05

Total Pages: 296

ISBN-13:

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Weak convergence of probability measures and uniformity classes; Fourier transforms and expansions of characteristic functions; Bounds for errors of normal approximation; Asymptotic expansions-nonlattice distributions; Asymptotic expansions - lattice distributions.

Asymptotic Expansions for Ordinary Differential Equations
Asymptotic Expansions for Ordinary Differential Equations

Author: Wolfgang Wasow

Publisher: Courier Dover Publications

Published: 2018-03-21

Total Pages: 385

ISBN-13: 0486824586

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This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.

Asymptotic Approximations for Probability Integrals
Asymptotic Approximations for Probability Integrals

Author: Karl W. Breitung

Publisher: Springer

Published: 2006-11-14

Total Pages: 157

ISBN-13: 3540490337

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This book gives a self-contained introduction to the subject of asymptotic approximation for multivariate integrals for both mathematicians and applied scientists. A collection of results of the Laplace methods is given. Such methods are useful for example in reliability, statistics, theoretical physics and information theory. An important special case is the approximation of multidimensional normal integrals. Here the relation between the differential geometry of the boundary of the integration domain and the asymptotic probability content is derived. One of the most important applications of these methods is in structural reliability. Engineers working in this field will find here a complete outline of asymptotic approximation methods for failure probability integrals.

Asymptotic Approximations of Integrals
Asymptotic Approximations of Integrals

Author: R. Wong

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 561

ISBN-13: 1483220710

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Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.

Expansions and Asymptotics for Statistics
Expansions and Asymptotics for Statistics

Author: Christopher G. Small

Publisher: CRC Press

Published: 2010-05-07

Total Pages: 359

ISBN-13: 1420011022

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Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti