Use of reference distributions when dealing with unknown regression errors

Abstract

A problem of estimating regression coefficients is considered when the distribution of error terms is unknown but symmetric. We propose the use of reference distributions having various kurtosis values. It is assumed that the true error distribution is one of the reference distributions, but the indicator variable for the true distribution is missing. The generalized expectation–maximization algorithm combined with a line search is developed for estimating regression coefficients. Simulation experiments are carried out to compare the performance of the proposed approach with some existing robust regression methods including least absolute deviation, Lp, Huber M regression and an approximation using normal mixtures under various error distributions. As the error distribution is far from a normal distribution, the proposed method is observed to show better performance than other methods.

Keywords:

• EM algorithm
• maximum likelihood
• Newton method
• robust regression

Acknowledgements

This work was supported by MOST (KOSEF) through the National Core Research Center for Systems Bio-Dynamics at POSTECH.