A Robust Estimator in Ridge Regression

We propose a robust estimator in ridge regression using the least trimmed squares. We call this estimator the ridge least trimmed squares estimator(RLTSE). We show that RLTSE has a high breakdown point, and develop an algorithm for the proposed estimates. The algorithm is very fast and the convergence of the algorithm can be proved. Simulations are performed to compare the efficiencies of RLTSE with that of the ridge least squares estimator. The results show that the former is more efficient than the latter when the errors have outliers or leverages. And a numerical example is given to illustrate the effectiveness of the proposed estimate.