Asymptotic Expansions of Some Mixtures of the Multivariate Normal Distribution and Their Error Bounds
Year: 1989
Type: article
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.
Source: The Annals of Statistics
Authors: Yasunori Fujikoshi, Ryoichi Shimizu
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2030717149