Optimal goodness-of-fit tests for normality against skewness and kurtosis alternatives
Three test statistics for the composite goodness-of-fit hypothesis of normality are presented. The proposed statistics are sums of squared L- statistics, and under the null hypothesis converge in distribution to chi-squared random variables. Further, the test procedures are asymptotically optimal for sequences of local skewness and/or kurtic alternative to the null hypothesis. The results of a simulation study indicate that the asymptotic critical values for the test procedures provide a useful approximation in samples as small as 25, and that the procedures compare favorably to existing tests in small samples.
composite goodness-of-fit hypothesis of normality
scientific article; zbMATH DE number 3940415
scientific article