Hiroshima Mathematical Journal

Computable error bounds for asymptotic expansions of the hypergeometric function ${}_1F_1$ of matrix argument and their applications

Yasunori Fujikoshi

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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.

Article information

Source
Hiroshima Math. J., Volume 37, Number 1 (2007), 13-23.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1176324092

Digital Object Identifier
doi:10.32917/hmj/1176324092

Mathematical Reviews number (MathSciNet)
MR2308521

Zentralblatt MATH identifier
1116.62026

Subjects
Primary: 62H10: Distribution of statistics
Secondary: 62E20: Asymptotic distribution theory

Keywords
Applications asymptotic expansions error bounds ${}_1F_1$ hypergeometric functions matrix argument

Citation

Fujikoshi, Yasunori. Computable error bounds for asymptotic expansions of the hypergeometric function ${}_1F_1$ of matrix argument and their applications. Hiroshima Math. J. 37 (2007), no. 1, 13--23. doi:10.32917/hmj/1176324092. https://projecteuclid.org/euclid.hmj/1176324092


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