Testing goodness-of-fit, independence and MCAR on incomplete dataset utilising the properties of non-degenerate and weakly-degenerate U- and V-statistics

Abstract

The talk focuses on utilization of properties of U- and V-statistics for statistical testing on incomplete dataset. First, a novel test for MCAR is presented, which is based on the properties of non-degenerate U-statistics. Second, asymptotic distribution of Kendall’s tau is derived under MCAR data and median imputation, relying on theory of De Wet and Randles for non-degenerate U-statistics with estimated parameters. Finally, properties of weakly-degenerate V-statistics are studied under MCAR data in the context of a well-known BHEP test for multivariate normality. Some conclusions are drawn and recommendations for practical applications are given.