A performance counterexample of Billor-Chatterjee-Hadi procedure and an improvement proposal for robust regression

The BCH procedure introduced by Billor et al. for fitting linear models was found to be inefficient for y-outliers in the presence of a high perturbation level. We propose to modify the first step of the BCH procedure, so that the robust distances are computed on the matrix Z=(y, X) of the basic subset. The performance of the present note procedure (PNP), as compared to the BCH procedure and the OLS method, was studied by processing several datasets used in the literature for robust regression and by performing a Monte Carlo experiment. PNP performs better particularly with datasets having high perturbation.