The moment-corrected phi-divergence test statistics for symmetry

In this paper we consider the family of φ -divergence test statistics, T n φ , S , for the problem of symmetry in I × I contingency tables whose asymptotic distribution is chi-square with I ( I - 1 ) / 2 degrees of freedom and we propose a moment-corrected φ -divergence test statistic in order to improve the accuracy of the chi-square approximation of the distribution of T n φ , S under the hypothesis of symmetry.