Estimation parameters using bisquare weighted robust ridge regression BRLTS estimator in the presence of multicollinearity and outliers

This study presents an improvement to robust ridge regression estimator. We proposed two methods Bisquare ridge least trimmed squares (BRLTS) and Bisquare ridge least absolute value (BRLAV) based on ridge least trimmed squares RLTS and ridge least absolute value (RLAV) respectively. We compared these methods with existing estimators, namely ordinary least squares (OLS) and Bisquare ridge regression (BRID) using three criteria: Bias, Root Mean Square Error (RMSE) and Standard Error (SE) to estimate the parameters coe±cients. The results of Bisquare ridge least trimmed squares (BRLTS) and Bisquare ridge least absolute value (BRLAV) are compared with existing methods using real data and simulation study. The empirical evidence shows that the results obtain from the BRLTS are the best among the three estimators followed by BRLAV with the least value of the RMSE for the diÆerent disturbance distributions and degrees of multicollinearity

Discussion of "The power of monitoring"

This is an invited comment on the discussion paper "The power of monitoring: how to make the most of a contaminated multivariate sample" by A. Cerioli, M. Riani, A. Atkinson and A. Corbellini that will appear in the journal Statistical Methods & Applications