Tests based on φ-divergences for bivariate symmetry

Abstract

In this paper we introduce a family of test statistics for testing symmetry based on φ-divergence families. These test statistics yield the likelihood ratio test and the Pearson test statistic as special cases. Asymptotic distribution for the new test statistics are derived under both the null and the alternative hypotheses. A simulation study is presented to see that some new test statistics offer an attractive alternative to the classical Pearson test statistic for the problem of symmetry.