An L1 estimation algorithm with degeneracy and linear constraints

M. Shi; M.A. Lukas

doi:10.1016/S0167-9473(01)00049-4

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An L1 estimation algorithm with degeneracy and linear constraints

Journal article

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An L1 estimation algorithm with degeneracy and linear constraints

M. Shi and M.A. Lukas

Computational Statistics & Data Analysis, Vol.39(1), pp.35-55

2002

DOI: https://doi.org/10.1016/S0167-9473(01)00049-4

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Abstract

An implementation of the reduced gradient algorithm is proposed to solve the linear L1 estimation problem (least absolute deviations regression) with linear equality or inequality constraints, including rank deficient and degenerate cases. Degenerate points are treated by solving a derived L1 problem to give a descent direction. The algorithm is a direct descent, active set method that is shown to be finite. It is geometrically motivated and simpler than the projected gradient algorithm (PGA) of Bartels, Conn and Sinclair, which uses a penalty function approach for the constrained case. Computational experiments indicate that the proposed algorithm compares favourably, both in reliability and efficiency, to the PGA, to the algorithms ACM551 and AFK (which use an LP formulation of the L1 problem) and to LPASL1 (which is based on the Huber approximation method of Madsen, Nielsen and Pinar). Although it is not as efficient as ACM552 (Barrodale–Roberts algorithm) on large scale unconstrained problems, it performs better on large scale problems with bounded variable constraints.

Details

Title: An L1 estimation algorithm with degeneracy and linear constraints
Authors/Creators: M. Shi (Author/Creator) - Murdoch University
M.A. Lukas (Author/Creator) - Murdoch University
Publication Details: Computational Statistics & Data Analysis, Vol.39(1), pp.35-55
Publisher: Elsevier
Identifiers: 991005541509907891
Copyright: © 2002 Elsevier Science B.V
Murdoch Affiliation: School of Chemical and Mathematical Science
Language: English
Resource Type: Journal article

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Citation topics: 9 Mathematics; 9.92 Statistical Methods; 9.92.220 Robust Estimation
Web Of Science research areas: Computer Science, Interdisciplinary Applications; Statistics & Probability
ESI research areas: Mathematics