Cluster-based L2L2 re-weighted regression

A simple robust L2L2-regression estimator is presented. The proposed method blends a minimum covariance determinant (MCD)(MCD) concentration algorithm with a controlled ordinary least squares regression phase. A hierarchical cluster analysis then partitions the data into main cluster of “half set” and a minor cluster of one or more groups. An initial least squares regression estimate arises from the main cluster of “half set”. Thereafter, a group-additive difference in fit statistic is used to activate the minor cluster and a controlled re-weighted least squares regression yields a robust efficient estimator with high breakdown value. Simulation experiment shows the advantage of the proposed method over the popular robust regression techniques in terms of robustness of coefficients, and blending outlier diagnostic procedure with parameter estimation.