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Volume 13, Issue 2
Huber's M-Estimator on Underdetermined Problems

Jiao-Song Wang & Sheng-Rong Tang

J. Comp. Math., 13 (1995), pp. 130-143.

Published online: 1995-04

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  • Abstract

After surveying the theoretical aspects of Huber's $M$-estimator on underdetermined problems, two finite algorithms are presented. Both proceed in a constructive manner by moving from one partition to an adjacent one. One of the algorithm, which uses the tuning constant as a continuation parameter, also has the facility to simultaneously estimate the tuning constant and scaling factor. Stable and efficient implementation of the algorithms is presented together with numerical results. The $L_1$-norm problem is mentioned as a special case.

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@Article{JCM-13-130, author = {Wang , Jiao-Song and Tang , Sheng-Rong}, title = {Huber's M-Estimator on Underdetermined Problems}, journal = {Journal of Computational Mathematics}, year = {1995}, volume = {13}, number = {2}, pages = {130--143}, abstract = {

After surveying the theoretical aspects of Huber's $M$-estimator on underdetermined problems, two finite algorithms are presented. Both proceed in a constructive manner by moving from one partition to an adjacent one. One of the algorithm, which uses the tuning constant as a continuation parameter, also has the facility to simultaneously estimate the tuning constant and scaling factor. Stable and efficient implementation of the algorithms is presented together with numerical results. The $L_1$-norm problem is mentioned as a special case.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9256.html} }
TY - JOUR T1 - Huber's M-Estimator on Underdetermined Problems AU - Wang , Jiao-Song AU - Tang , Sheng-Rong JO - Journal of Computational Mathematics VL - 2 SP - 130 EP - 143 PY - 1995 DA - 1995/04 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9256.html KW - AB -

After surveying the theoretical aspects of Huber's $M$-estimator on underdetermined problems, two finite algorithms are presented. Both proceed in a constructive manner by moving from one partition to an adjacent one. One of the algorithm, which uses the tuning constant as a continuation parameter, also has the facility to simultaneously estimate the tuning constant and scaling factor. Stable and efficient implementation of the algorithms is presented together with numerical results. The $L_1$-norm problem is mentioned as a special case.

Wang , Jiao-Song and Tang , Sheng-Rong. (1995). Huber's M-Estimator on Underdetermined Problems. Journal of Computational Mathematics. 13 (2). 130-143. doi:
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