Error bounds for asymptotic expansions of Wilks' lambda distribution

Yasunori Fujikoshi and Vladimir V. Ulyanov

Journal of Multivariate Analysis, 2006, vol. 97, issue 9, 1941-1957

Abstract: Let [Lambda]=Se/Se+Sh, where Sh and Se are independently distributed as Wishart distributions Wp(q,[Sigma]) and Wp(n,[Sigma]), respectively. Then [Lambda] has Wilks' lambda distribution [Lambda]p,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=-nlog[Lambda]. We derive error bounds for the approximations. It is necessary to underline that our error bounds are given in explicit and computable forms.

Keywords: Asymptotic; expansions; Error; bounds; Function; of; multivariate; scale; mixture; Wilks'; lambda; distribution; Wishart; distribution (search for similar items in EconPapers)
Date: 2006
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