Variable Selection in Multivariate Regression using Local Influence

A procedure for selecting regressors in multivariate regression using local influence is suggested. It assesses the effect of perturbation of regressors on the profile log-likelihood displacement under an appropriate perturbation scheme in order to select regressors. By starting a location model, the direction vector corresponding to the largest curvature of the profile log-likelihood displacement surface is first found and then select a regressor associated with the element of the above direction vector that has the largest absolute value. If the hypothesis that the regression coefficients for regressors not selected so far are zero is not significant, then the selection procedure stops, and otherwise, we proceed further. We provide a numerical example for illustration.