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

Authors:
M. Ç. Pinar
Affiliations:
Department of Industrial Engineering, Bilkent University, Ankara, Turkey
Venue:
Computing
Year:
2004

Citing 8
Cited 1

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Abstract

We review and extend previous work on the approximation of the linear l1 estimator by the Huber M-estimator based on the algorithms proposed by Clark and Osborne [7], and Madsen and Nielsen [12]. 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 l1 estimator from the Huber M-estimator in a finite number of steps without any restrictive steps nor assumptions. Summary computational results are given.