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.
Publié le : 1989-09-14
Classification:
Error bound,
asymptotic expansion,
distribution function,
scale mixture of the multivariate normal distribution,
MLE,
a general MANOVA model,
62H20,
62H10
@article{1176347259,
author = {Fujikoshi, Yasunori and Shimizu, Ryoichi},
title = {Asymptotic Expansions of Some Mixtures of the Multivariate Normal Distribution and Their Error Bounds},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 1124-1132},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347259}
}
Fujikoshi, Yasunori; Shimizu, Ryoichi. Asymptotic Expansions of Some Mixtures of the Multivariate Normal Distribution and Their Error Bounds. Ann. Statist., Tome 17 (1989) no. 1, pp. 1124-1132. http://gdmltest.u-ga.fr/item/1176347259/