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March 2007 Computable error bounds for asymptotic expansions of the hypergeometric function ${}_1F_1$ of matrix argument and their applications
Yasunori Fujikoshi
Hiroshima Math. J. 37(1): 13-23 (March 2007). DOI: 10.32917/hmj/1176324092

Abstract

In this paper we derive error bounds for asymptotic expansions of the hypergeometric functions ${}_1F_1(n; n+b; Z)$ and ${}_1F_1(n; n+b; -Z)$, where $Z$ is a $p \times p$ symmetric nonnegative definite matrix. The first result is applied for theoretical accuracy of approximating the moments of $\Lambda=|S_e|/|S_e+S_h|$, where $S_h$ and $S_e$ are independently distributed as a noncentral Wishart distribution $W_p(q, \Sigma, \Sigma^{1/2} \Omega \Sigma^{1/2})$ and a central Wishart distribution $W_p(n, \Sigma)$, respectively. The second result is applied for theoretical accuracy of approximating the probability density function of the maximum likelihood estimators of regression coefficients in the growth curve model.

Citation

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Yasunori Fujikoshi. "Computable error bounds for asymptotic expansions of the hypergeometric function ${}_1F_1$ of matrix argument and their applications." Hiroshima Math. J. 37 (1) 13 - 23, March 2007. https://doi.org/10.32917/hmj/1176324092

Information

Published: March 2007
First available in Project Euclid: 11 April 2007

zbMATH: 1116.62026
MathSciNet: MR2308521
Digital Object Identifier: 10.32917/hmj/1176324092

Subjects:
Primary: 62H10
Secondary: 62E20

Rights: Copyright © 2007 Hiroshima University, Mathematics Program

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Vol.37 • No. 1 • March 2007
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