Berry–Esseen bound for high dimensional asymptotic approximation of Wilks’ Lambda distribution

Let Λ=|Se|/|Se+Sh|Λ=|Se|/|Se+Sh|, where ShSh and SeSe are independently distributed as Wishart distributions Wp(q,Σ)Wp(q,Σ) and Wp(n,Σ)Wp(n,Σ), respectively. Then ΛΛ is distributed as Wilks’ lambda distribution Λp,q,nΛp,q,n which appears as the distributions of various multivariate likelihood ratio tests. In this paper, we derive a Berry–Essen bound for a high dimensional asymptotic approximation of the distribution of T=-nlogΛ when p/n→c∈(0,1)p/n→c∈(0,1).