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Saddlepoint approximations: A review and some new applications


Paolella, Marc S; Broda, Simon (2012). Saddlepoint approximations: A review and some new applications. In: Gentle, James E; Härdle, Wolfgang K; Mori, Yuichi. Handbook of Computational Statistics : Concepts and Methods. Berlin: Springer (Bücher), 953-984.

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 $M_{X}(s)$, where s is the real argument of the function, such that s is contained in the convergence strip of $M_{X}(s)$, 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.

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 $M_{X}(s)$, where s is the real argument of the function, such that s is contained in the convergence strip of $M_{X}(s)$, 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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Additional indexing

Item Type:Book Section, refereed, further contribution
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Physical Sciences > General Computer Science
Scope:Discipline-based scholarship (basic research)
Language:English
Date:2012
Deposited On:12 Mar 2012 12:03
Last Modified:20 Apr 2024 03:31
Publisher:Springer (Bücher)
Series Name:Springer Handbooks of Computational Statistics
Number:2nd editio
ISSN:2197-9790
ISBN:978-3-642-21550-6
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/978-3-642-21551-3_32
Related URLs:http://www.springer.com/statistics/computational+statistics/book/978-3-642-21550-6
Other Identification Number:merlin-id:6861
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