On the Effects of Moderate Multivariate Nonnormality on Roy's Largest Root Test
研究了在多元Edgeworth总体中，Roy最大根统计量的渐近分布展开到一阶项，用Mardia偏度和峰度度量表达非正态性影响，并给出k样本MANOVA情形下名义显著性水平的修正表。
Abstract The asymptotic distribution of Roy's largest root statistic in multivariate Edgeworth populations is expanded to terms of the first order. To this order, the effects of non-normality are expressed by Mardia's measures of multivariate skewness and kurtosis, together with a supplementary skewness measure. Tables of corrections to the nominal significance level are presented for the k-sample MANOVA situation. Comparison with simulation results indicates that the correction terms provide a useful indication both of the magnitude and the direction of the effect of nonnormality on the nominal 5 percent Type I error, even when the underlying population is not well represented by an Edgeworth expansion, provided that the skewness and kurtosis are not too large. Key Words: Roy's largest root testMultivariate skewness and kurtosisMANOVALinear differential equationsDoubly noncentral beta distribution