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Finite Computation of the ℓ1 Estimator from Huber’s M-Estimator in Linear Regression

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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.

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  1. Department of Industrial Engineering, Bilkent University, 06533, Ankara, Turkey

    M. Ç. P⊂nar

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  1. M. Ç. P⊂nar
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Correspondence to M. Ç. P⊂nar.

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P⊂nar, M. Finite Computation of the ℓ1 Estimator from Huber’s M-Estimator in Linear Regression. Computing 72, 365–384 (2004). https://doi.org/10.1007/s00607-003-0035-1

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  • DOI: https://doi.org/10.1007/s00607-003-0035-1

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