Distributions of a Class of Statistics Useful in Multivariate Analysis
研究了一类矩具有特定形式的统计量的精确分布和渐近分布，应用于检验线性假设的Wilks准则，数值比较表明其渐近展开的首项优于Box的卡方分布渐近展开，且精确分布易于计算并具有稳定的递推关系。
Abstract In this article, exact and asymptotic distributions of a class of statistics whose moments are of a particular form have been obtained. An application to Wilks's criterion for testing a linear hypothesis is given, and it is shown by numerical comparison that the first term of the asymptotic expansion of the distribution obtained in this article is better than Box's asymptotic expansion in terms of chisquared distributions. The exact distribution is easily computable and has the distinct advantage that stable recurrence relations exist between the coefficients involved.