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Saddlepoint Approximations: A Review and Some New Applications

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Handbook of Computational Statistics

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

The saddlepoint method of approximation is attributed to Daniels (1954), and can be described in basic terms as yielding an accurate and usually fast and very numerically reliable approximation to the mass or density function (hereafter pdf), and the cumulative distribution function (cdf), of a random variable, say X, based on knowledge of its moment generating function (mgf). Denote the latter by \({\mathbb{M}}_{X}(s)\), where s is the real argument of the function, such that s is contained in the convergence strip of \({\mathbb{M}}_{X}(s)\), to be defined below. Several surveys and monographs are available; the best starting point is the currently definitive exposition in Butler (2007), along with the first textbook dedicated to the subject, Jensen (1995). Our goal is to outline the basics of the methodology in the easiest way possible, and then to illustrate a small subset of its many applications.

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Authors and Affiliations

  1. Department of Quantitative Economics, University of Amsterdam, Amsterdam, The Netherlands

    Simon A. Broda

  2. Swiss Banking Institute, University of Zurich, Zurich, Switzerland

    Marc S. Paolella

  3. Swiss Finance Institute, Zurich, Switzerland

    Marc S. Paolella

Authors
  1. Simon A. Broda
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  2. Marc S. Paolella
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Correspondence to Simon A. Broda .

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Editors and Affiliations

  1. Dept. Computational & Data, Sciences, George Mason University, University Drive 4400, Fairfax, 22030-4444, Virginia, USA

    James E. Gentle

  2. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  3. Dept. Socioinformation, Okayama University, Ridai-cho 1-1, Okayama, 700-0005, Japan

    Yuichi Mori

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Broda, S.A., Paolella, M.S. (2012). Saddlepoint Approximations: A Review and Some New Applications. In: Gentle, J., Härdle, W., Mori, Y. (eds) Handbook of Computational Statistics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21551-3_32

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