Laplace approximations to hypergeometric functions of two matrix arguments

Authors:
Ronald W. Butler;Andrew T. A. Wood
Affiliations:
Department of Statistics, Colorado State University, Fort Collins, CO;School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
Venue:
Journal of Multivariate Analysis
Year:
2005

Citing 1
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Abstract

We present a unified approach to Laplace approximation of hypergeometric functions with two matrix arguments. The general form of the approximation is designed to exploit the Laplace approximations to hypergeometric functions of a single matrix argument presented in Butler and Wood (Ann. Statist. 30 (2002) 1155, Laplace approximations to Bessel functions of matrix argument, J. Comput. Appl. Math. 155 (2003) 359) which have proved to be very accurate in a variety of settings. All but one of the approximations presented here appear to be new. Numerical accuracy is investigated in a number of statistical applications.