Empirical likelihood based hypothesis testing

Abstract

Omnibus tests for various nonparametric hypotheses are developed using the empirical likelihood method. These include tests for symmetry about zero, changes in distribution, independence and exponentiality. The approach is to localize the empirical likelihood using a suitable `time' variable implicit in the null hypothesis and then form an integral of the log-likelihood ratio statistic. The asymptotic null distributions of these statistics are established. In simulation studies, the proposed statistics are found to have greater power than corresponding Cram\'er--von Mises type statistics.