The use of U-statistics for testing normality against alternatives with both tails heavy or both tails light

Abstract

U –statistics are used to construct statistics for testing normality against alternatives that have both tails heavy or both tails light. One resulting test statistic is equivalent to D'Agostino's D , and insights on the nature of D are given through the U –statistic approach. A Monte Carlo power study is reported, which includes D , another statistic derived from the U –statistic approach, a statistic suggested by Hogg for use in adaptive inference, the sample kurtosis, and the range divided by the sample standard deviation.