Subset selection in multiple linear regression in the presence of outlier and multicollinearity

Various subset selection methods are based on the least squares parameter estimation method. The performance of these methods is not reasonably well in the presence of outlier or multicollinearity or both. Few subset selection methods based on the M-estimator are available in the literature for outlier data. Very few subset selection methods account the problem of multicollinearity with ridge regression estimator. In this article, we develop a generalized version of S-p statistic based on the jackknifed ridge M-estimator for subset selection in the presence of outlier and multicollinearity. We establish the equivalence of this statistic with the existing C-p, S-p and R-p statistics. The performance of the proposed method is illustrated through some numerical examples and the correct model selection ability is evaluated using simulation study. (C) 2014 Elsevier B.V. All rights reserved.