Subset Selection in Multiple Linear Regression for Non-normal Symmetric Error Terms

摘要

Various methods for subset selection in multiple linear regression are available in literature. Most of the methods are based on the least squares estimator. The performance of the subset selection methods based on the least squares estimator is not reasonably well when the error distribution is non-normal. And hence, these methods fail to select the correct subset model. In this article, we propose a method for subset selection in multiple linear regression when the error distribution is non-normal. Rank based parameter estimation method is used for the estimation of regression parameters. The sampling distribution of proposed statistic is obtained through simulation study. Laplace, Student's t, Slash and Cauchy distribution are considered for the error term to evaluate the performance of the proposed method. Also, a stepwise procedure for subset selection is proposed and illustrated with an example.