Robust Regression Using the t-distribution and the EM Algorithm

Abstract

The paper deals with a linear regression model. The EM algorithm is popular tool for maximum likelihood estimation of the parameters of regression model. It provides a method of robust regression under the assumption that the disturbances are independent and have identical multivariate t distribution.

Previous work focused on the method of maximum likelihood estimation via the EM algorithm under the assumption that the degrees of freedom parameter of the t distribution is a scalar. In this paper, a broader assumption is employed, namely, that the disturbances have a multivariate t distribution with a vector of degrees of freedom. Missing values from the EM algorithm are random matrices.

The theoretical results are illustrated in a simulation experiment using several distributions for the error process. Robust procedures are shown to be superior to the method of least squares.