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Saddlepoint approximations with applications. (English) Zbl 1183.62001

Cambridge Series in Statistical and Probabilistic Mathematics 22. Cambridge: Cambridge University Press (ISBN 978-0-521-87250-8/hbk). xi, 564 p. (2007).
Publisher’s description: Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from a user’s point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1–6 at an elementary mathematical level. Chapters 7–9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.
This book is an accessible, readable introduction that equips the reader to use the methods for real applications. It contains abundant examples, both numerical and theoretical, building and reinforcing skills and understanding. The author is a major contributor to the field.

MSC:

62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
65C60 Computational problems in statistics (MSC2010)
62E20 Asymptotic distribution theory in statistics
62E17 Approximations to statistical distributions (nonasymptotic)
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