Asymptotic expansions of the null distributions of three test statistics in a nonnormal {GMANOVA} model
Hirokazu Yanagihara · Hiroshima Mathematical Journal · 2001
Astrt.This paper deals with three test statistics for testing a linear hypothesis and estimators of regression coe½cients in the GMANOVA model which was proposed by Potthof and Roy (1964), without assuming normal error.The test statistics considered include the likelihood ratio statistic, the Lawley-Hotelling trace criterion and the Bartlett-Nanda-Pillai trace criterion, which have been proposed under normality.We obtain asymptotic expansions of the null distributions of three test statistics up to the order n À1 , where n is the sample size.The results are generalizations of the formulas in Wakaki, Yanagihara and Fujikoshi (2000).In addition, asymptotic expansions of the distribution functions of several standardized statistics on regression coe½cients are derived.