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September, 1989 Asymptotic Expansions of Some Mixtures of the Multivariate Normal Distribution and Their Error Bounds
Yasunori Fujikoshi, Ryoichi Shimizu
Ann. Statist. 17(3): 1124-1132 (September, 1989). DOI: 10.1214/aos/1176347259

Abstract

This paper deals with the distribution of $\mathbf{X} = \sum^{1/2}\mathbf{Z}$, where $\mathbf{Z}: p \times 1$ is distributed as $N_p(0, I_p), \sum$ is a positive definite random matrix and $\mathbf{Z}$ and $\sum$ are independent. Assuming that $\sum = I_p + BB'$, we obtain an asymptotic expansion of the distribution function of $\mathbf{X}$ and its error bound, which is useful in the situation where $\sum$ tends to $I_p$. A stronger version of the expansion is also given. The results are applied to the asymptotic distribution of the MLE in a general MANOVA model.

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Yasunori Fujikoshi. Ryoichi Shimizu. "Asymptotic Expansions of Some Mixtures of the Multivariate Normal Distribution and Their Error Bounds." Ann. Statist. 17 (3) 1124 - 1132, September, 1989. https://doi.org/10.1214/aos/1176347259

Information

Published: September, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0681.62033
MathSciNet: MR1015141
Digital Object Identifier: 10.1214/aos/1176347259

Subjects:
Primary: 62H20
Secondary: 62H10

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 3 • September, 1989
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