Error bounds for asymptotic expansions of Wilks' lambda distribution

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.