SPARSE LEAST TRIMMED SQUARES REGRESSION FOR ANALYZING HIGH-DIMENSIONAL LARGE DATA SETS

• 成果类型: Article
• 署名作者: Alfons, Andreas; Croux, Christophe; Gelper, Sarah
• 署名单位: KU Leuven; Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/12-AOAS575
• 发表日期: 2013
• 页码: 226-248
• 关键词: VARIABLE SELECTION; Lasso; shrinkage

摘要

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.