Computing the constrained M-estimates for regression
Constrained M-estimates for regression have been previously proposed as an alternative class of robust regression estimators with high breakdown point and high asymptotic efficiency. These are closely related to S-estimates, and it is shown that in some cases they will necessarily coincide. It has been difficult to use the CM-estimators in practice for two reasons. Adequate computational methods have been lacking and there has also been some confusion concerning the tuning parameters. Both of these problems are addressed; an updated table for choice of suitable parameter value is given, and an algorithm to compute CM-estimates for regression is presented. It can also be used to compute S-estimates. The computational problem to be solved is global optimization with an inequality constraint. The algorithm consists of two phases. The first phase is finding suitable starting values for the local optimization. The second phase, the efficient finding of a local minimum, is described in more detail. There is a MATLAB code generally available from the net. A Monte Carlo simulation is performed, using this code, to test the performance of the estimator as well as the algorithm.
robust regression robustness cm-estimates algorithms s-estimates high breakdown point estimators for regression