The Asymptotic Equivalence of Some Modified Shapiro-Wilk Statistics-- Complete and Censored Sample Cases

Abstract

The Shapiro-Wilk statistic and its modifications are widely applied in tests for normality. We establish the asymptotic equivalence of a class of statistics based on different choices of normal scores. In particular, we conclude that the Shapiro-Francia, Filliben, Weisberg-Bingham and de Wet-Venter versions of the statistic are asymptotically equivalent. Our results also apply to the Type I and Type II censored data cases.