Asymptotic expansion of the null distribution of the likelihood ratio statistic for testing the equality of variances in a nonnormal one-way {ANOVA} model

Abstract

This paper is concerned with the null distribution of the likelihood ratio statistic for testing the equality of variances of q nonnormal populations. It is known that the null distribution of this statistic converges to w q 1 under normality. We extend this result by obtaining an asymptotic expansion under general conditions. Numerical accuracies are studied for some approximations of the percentage points and actual test sizes of this statistic based on the limiting distribution and the asymptotic expansion.