Robustness of Correlation Coefficient and Variance Ratio under Elliptical Symmetry

Abstract

Parametric robustness of a statistic in a class of distributions implies that the distribution of the statistic is the same for any member of the class of distributions. The bivariate Wishart distribution, based on the class of bivariate elliptical distributions, involves three essential statistics, namely, two sample variances and the product moment correlation coefficient. The distribution of the product moment correlation coefficient is known to be robust in the class of bivariate elliptical distributions. In this paper, we prove that the distribution of the variance ratio is also robust in the class of bivariate elliptical distributions.