Robust testing procedures for scale differences in paired data

Abstract

Several statistical tests have been proposed in the literature to assess the difference between two scale parameters in paired data. If the location parameters of each sample are different, many of these test statistics are adjusted using the estimated location parameters. Then, the performance of the test statistics depends on the selection of the location estimators. In this study, the asymptotically distribution-free test based on the U-statistic, which does not depend on two location parameters, is constructed. The asymptotic normality and the asymptotic power of the proposed test are examined. Furthermore, the proposed test is compared with the existing tests in terms of Pitman's asymptotic relative efficiency. To improve the Type I error rate in the small sample size, the robust test procedure based on the percentile bootstrap is also proposed. Our simulation studies show that the Type I error rate of the proposed test is more controlled and robust than existing tests in many situations. Further, the empirical power of the proposed test is shown to be high for heavy-tailed or asymmetric distributions.