Abstract
Asymptotic non-null distribution of the likelihood ratio criterion for testing the linear hypothesis in multivariate analysis is obtained up to the order $N^{-2}$, where $N$ means the sample size, by using the characteristic function expressed in terms of hypergeometric function with matrix argument. This result holds without any assumption on the rank of non-centrality matrix. Asymptotic non-null distribution of the likelihood ratio criterion for independence between two sets of variates is also obtained up to the order $N^{-1}$.
Citation
Nariaki Sugiura. Yasunori Fujikoshi. "Asymptotic Expansions of the Non-Null Distributions of the Likelihood Ratio Criteria for Multivariate Linear Hypothesis and Independence." Ann. Math. Statist. 40 (3) 942 - 952, June, 1969. https://doi.org/10.1214/aoms/1177697599
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