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March 2013 Sparse least trimmed squares regression for analyzing high-dimensional large data sets
Andreas Alfons, Christophe Croux, Sarah Gelper
Ann. Appl. Stat. 7(1): 226-248 (March 2013). DOI: 10.1214/12-AOAS575

Abstract

Sparse model estimation is a topic of high importance in modern data analysis due to the increasing availability of data sets with a large number of variables. Another common problem in applied statistics is the presence of outliers in the data. This paper combines robust regression and sparse model estimation. A robust and sparse estimator is introduced by adding an $L_{1}$ penalty on the coefficient estimates to the well-known least trimmed squares (LTS) estimator. The breakdown point of this sparse LTS estimator is derived, and a fast algorithm for its computation is proposed. In addition, the sparse LTS is applied to protein and gene expression data of the NCI-60 cancer cell panel. Both a simulation study and the real data application show that the sparse LTS has better prediction performance than its competitors in the presence of leverage points.

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Andreas Alfons. Christophe Croux. Sarah Gelper. "Sparse least trimmed squares regression for analyzing high-dimensional large data sets." Ann. Appl. Stat. 7 (1) 226 - 248, March 2013. https://doi.org/10.1214/12-AOAS575

Information

Published: March 2013
First available in Project Euclid: 9 April 2013

zbMATH: 06171270
MathSciNet: MR3086417
Digital Object Identifier: 10.1214/12-AOAS575

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.7 • No. 1 • March 2013
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