Error bounds for asymptotic expansions of Wilks' lambda distribution

Authors:
Yasunori Fujikoshi;Vladimir V. Ulyanov
Affiliations:
Graduate School of Science and Engineering, Chuo University, Bunkyou-ku, Tokyo, Jupan;Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia
Venue:
Journal of Multivariate Analysis - Special issue dedicated to Professor Yasunori Fujikoshi
Year:
2006

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Abstract

Let Λ = |Se|/|Se+Sh|, where Sh and Se are independently distributed as Wishart distributions Wp (q, Σ) and Wp (n, Σ), respectively. Then Λ has Wilks' lambda distribution Λp,q,n which appears as the distributions of various multivariate likelihood ratio tests. This paper is concerned with theoretical accuracy for asymptotic expansions of the distribution of T =-n log Λ. We derive error bounds for the approximations. It is necessary to underline that our error bounds are given in explicit and computable forms.