Error bounds for asymptotic expansions of Wilks’ lambda distribution

Let Λ = | S e | / | S e + S h | , where S h and S e are independently distributed as Wishart distributions W p ( q , Σ ) and W p ( n , Σ ) , respectively. Then Λ has Wilks’ lambda distribution Λ 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 = - 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.