Abstract
SYNOPTIC ABSTRACTIt is well known that Bartlett adjustment yields an improvement on the chi-squared approximation to the likelihood ratio statistic. However, there exist some multivariate tests for which such an improvement is not possible by a usual Bartlett adjustment. Typical examples are the Lawley-Hotelling trace criterion and the Bartlett-Nanda-Pillai trace criterion for testing the multivariate linear hypothesis under normality. The purpose of this paper is to improve the large-sample chi-squared approximation to a general statistic T including these test statistics by constructing a monotone function = Qn(T).
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