Full Bayesian Empirical Likelihood Significance Test for Equality Of Medians

This paper discusses the empirical likelihood ratio test for testing equality of medians of two distributions. Yu et al. (2011) proposed four forms of empirical likelihood ratio test for testing this hypothesis and one of them is based on the pooled sample median. The asymptotic distribution of the test statistic as derived in Yu et al (2011) differ from the one obtained in Nimbalkar and Rajarshi (1997). The numerical investigation of the present paper supports the result of Nimbalkar and Rajarshi (1997) for distributions belonging to the symmetric location scale families. Full Bayesian significance test is derived to test sharp null hypothesis. In the empirical likelihood set up, full Bayesian significance test cannot be directly derivable. Using a novel idea we extend full Bayesian significant test for the case of empirical likelihood. This is the hybrid test and shares the features of parametric and nonparametric tests and can be used even in sample surveys.