Jackknife Empirical Likelihood Methods for Testing the Distributional Symmetry

Abstract

In this talk, we consider a general k -th correlation coefficient between the density function and distribution function of a continuous variable as a measure of symmetry and asymmetry. We make statistical inference of the k -th correlation coefficient by using jackknife empirical likelihood (JEL) and its variations to construct confidence intervals. The JEL statistic is shown to be asymptotically a standard chi-squared distribution. We compare our methods to the previous empirical likelihood (EL) techniques of [1] and show the JEL possesses better small sample properties compared with existing methods. Simulation studies are conducted to examine the performance of the proposed estimators. We also use our proposed methods to analyze two real datasets for illustration.