Aspects Of M-Estimation And l-Fitting Problems

Mathematics Research Report MRR95-058

Aspects Of M-Estimation And l-Fitting Problems

M.R. Osborne and G.A. Watson

Abstract: There has been a recent flurry of interest in the properties of the Huber M-estimator and its relation to l₁ fitting. In particular, it has been shown that the dual of the M-estimation problem is an interval constrained quadratic program.Thus methods for solving such quadratic programs can be applied directly to the M-estimation problem, and existing methods such as Clark's partitioning algorithm can be interpreted in the dual framework. Also, the duality result has been applied to study the limiting behavior of the M-estimator as the scale parameter $\gamma\to 0$, and results have been reported which claim that the l₁ fitting problem should be solved as the limiting case of M-estimation as $\gamma \to 0$. This claim is reviewed, and it is concluded that its basis is by no means as clear cut as has been suggested.

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