On testing the class of symmetry using entropy characterization and empirical likelihood approach

TL;DR

This paper introduces new nonparametric tests for symmetry based on entropy characterization and empirical likelihood, demonstrating superior finite sample performance through simulations and real data applications.

Contribution

It develops novel symmetry tests using entropy characterization and jackknife empirical likelihood, with proven asymptotic properties and improved performance over existing methods.

Findings

Jackknife empirical likelihood tests outperform existing symmetry tests.

Proposed tests have desirable asymptotic properties.

Real data analysis confirms practical applicability.

Abstract

In this paper, we obtain a new characterization result for symmetric distributions based on the entropy measure. Using the characterization, we propose a nonparametric test to test the symmetry of a distribution. We also develop the jackknife empirical likelihood and the adjusted jackknife empirical likelihood ratio tests. The asymptotic properties of the proposed test statistics are studied. We conduct extensive Monte Carlo simulation studies to assess the finite sample performance of the proposed tests. The simulation results indicate that the jackknife empirical likelihood and adjusted jackknife empirical likelihood ratio tests show better performance than the existing tests. Finally, two real data sets are analysed to illustrate the applicability of the proposed tests.