Cauchy Regression and Confidence Intervals for the Slope

This paper uses computer simulations to verify several features of the Greatest Deviation (GD) nonparametric correlation coefficient. First, its asymptotic distribution is used in a simple linear regression setting where both variables are bivariate. Second, the distribution free property of GD is demonstrated using both the bivariate normal and bivariate Cauchy distributions. Third, the robustness of the method is shown by estimating parameters in the Cauchy case. Fourth, a general geometric method is used to estimate a ratio of scale factors used in the confidence interval. The methods in this paper are an outgrowth of general research on the use of nonparametric correlation coefficients in statistical estimations. The results in this paper are not specific to GD and are appropriate for other rank based correlation coefficients.