High leverage points and vertical outliers resistant model selection in regression

Abstract

It is necessary to consider only relevant predictor variables for prediction purpose because irrelevant predictors in the regression model will tend to misleading inference. There are so many model selection methods available in the literature; among these, some methods are resistant to vertical outliers, but still, the problem of the presence of vertical outliers and leverage points is not well studied. In this article, we have modified the Sp statistic using the generalized M-estimator for robust model selection in the presence of vertical outliers and high leverage points. The proposed model selection criterion selects only relevant predictor variables by probability one for a large sample size. We found the equivalence of this criterion and the existing Cp and Sp criteria. The superiority of a proposed criterion is demonstrated using simulated and real data.