On a Robust Subset Selection Procedure for the Slopes of Regression Equations

The problem of selection of a subset containing the largest of several slope parameters of regression equations is considered. The proposed selection procedure is based on the weighted median estimators for regression parameters and the median of rescaled absolute residuals for scale parameters. Those estimators are compared with the classical least squares estimators by a simulation study. A Monte Carlo comparison is also made between the new procedure based on the weighted median estiamtors and the procedure based on the least squares estimators. The results show that the proposed procedure is quite robust with respect to the heaviness of distribution tails.