Finite computation of the ℓ 1estimator from Huber's M-estimator in linear regression

Abstract

We review and extend previous work on the approximation of the linear ℓ 1 estimator by the Huber M-estimator based on the algorithms proposed by Clark and Osborne, and Madsen and Nielsen. Although the Madsen-Nielsen algorithm is a promising one, it is guaranteed to terminate finitely under certain assumptions. We describe a variant of the Madsen-Nielsen algorithm to compute the ℓ 1 estimator from the Huber M-estimator in a finite number of steps without any restrictive steps nor assumptions. Summary computational results are given.