Normal Approximation and Asymptotic Expansions

Normal Approximation and Asymptotic Expansions
Title Normal Approximation and Asymptotic Expansions PDF eBook
Author Rabi N. Bhattacharya
Publisher SIAM
Pages 333
Release 2010-11-11
Genre Mathematics
ISBN 089871897X

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Asymptotic Approximations of Integrals

Asymptotic Approximations of Integrals
Title Asymptotic Approximations of Integrals PDF eBook
Author R. Wong
Publisher Academic Press
Pages 561
Release 2014-05-10
Genre Mathematics
ISBN 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.

Normal Approximation and Asymptotic Expansions

Normal Approximation and Asymptotic Expansions
Title Normal Approximation and Asymptotic Expansions PDF eBook
Author Rabindra Nath Bhattacharya
Publisher Krieger Publishing Company
Pages 291
Release 1976
Genre Mathematics
ISBN 9780898746907

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Expansions and Asymptotics for Statistics

Expansions and Asymptotics for Statistics
Title Expansions and Asymptotics for Statistics PDF eBook
Author Christopher G. Small
Publisher CRC Press
Pages 359
Release 2010-05-07
Genre Mathematics
ISBN 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

Analytic Combinatorics

Analytic Combinatorics
Title Analytic Combinatorics PDF eBook
Author Philippe Flajolet
Publisher Cambridge University Press
Pages 825
Release 2009-01-15
Genre Mathematics
ISBN 1139477161

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Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Asymptotics and Borel Summability

Asymptotics and Borel Summability
Title Asymptotics and Borel Summability PDF eBook
Author Ovidiu Costin
Publisher CRC Press
Pages 266
Release 2008-12-04
Genre Mathematics
ISBN 1420070320

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Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. The author explains basic ideas, concepts, and methods of generalized Borel summability, tr

Series Approximation Methods in Statistics

Series Approximation Methods in Statistics
Title Series Approximation Methods in Statistics PDF eBook
Author John E. Kolassa
Publisher Springer Science & Business Media
Pages 162
Release 2013-04-17
Genre Mathematics
ISBN 1475742754

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This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field. In presenting expansion limit theorems I have drawn heavily 011 notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted.