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An improved saddlepoint approximation

Lookup NU author(s): Dr Colin Gillespie

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Abstract

Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm. © 2006 Elsevier Inc. All rights reserved.


Publication metadata

Author(s): Gillespie CS, Renshaw E

Publication type: Article

Publication status: Published

Journal: Mathematical Biosciences

Year: 2007

Volume: 208

Issue: 2

Pages: 359-374

ISSN (print): 0025-5564

ISSN (electronic): 1879-3134

Publisher: Elsevier Inc.

URL: http://dx.doi.org/10.1016/j.mbs.2006.08.026

DOI: 10.1016/j.mbs.2006.08.026

PubMed id: 17306841


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