A simulation study of a class of nonparametric test statistics: a close look of empirical distribution function-based tests

Kolmogorov–Smirnov (KS) statistic is a non-parametric based on the empirical distribution function. For one-sample case, it uses supremum distance between an function (EDF) and pre-specified cumulative (CDF). two-sample measures maximum of two EDFs. KS test, as well other EDF-based tests such Anderson-Darling (AD) test Cramer-von Mises (CvM) has been widely used in statistical analysis. To address compare performance these statistics, we have conducted simulation study comparing type I error power CvM AD Chi-squared test. Our includes both one sample for independent correlated samples. showed that if do not prior information about tested distributions, are better. However, so long density distributions bell-shaped expecting differences variance/sparseness, then may be more preferable. When correlation exists samples, adjustment informative size important required.