On the Effects of Moderate Multivariate Nonnormality on Wilks's Likelihood Ratio Criterion
研究了中等程度多元非正态性如何影响Wilks似然比准则，通过Edgeworth分布构建统计分布，发现非正态性下抽样分布的一阶近似涉及Mardia的偏度和峰度度量，并给出了5%水平下的修正项。
A technique for the formal construction of statistical distributions in multivariate Edgeworth populations is applied to investigate the effects of moderate multivariate nonnormality on the test statistics used in connexion with the general linear model, in particular, Wilks's likelihood ratio criterion. The first-order approximation to the sampling distributions under nonnormality are shown to involve Mardia's measures of multivariate skewness and kurtosis, together with a supplementary skewness measure. Correction terms for tests at the 5% level are constructed for one-way analysis of variance, and the resulting approximations are compared with simulation results for a range of bivariate distributions.