Ordinary least squares and maximum likelihood regression with cauchy errors

Abstract

In this paper, we'll examine the effect of Cauchy errors in a linear model on the performance of the least squares and maximum likelihood estimators with the aid of two factors; the sample size and the Cauchy scale parameter. A sampling distribution of one hundred experiments was done to judge the estimation process in the case of least squares method. On the other hand, multivariate Newton Raphson was used to calculate the unique solution of the partial derivatives of the log lokelihood function. The uniqueness of the solution is proved for a known location parameter and unknown scale parameter. At the end, a comparison is held based on the experimental methods done.