Sparse Least Trimmed Squares Regression
21 Pages Posted: 3 Dec 2011
Date Written: 2011
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 L1 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. Both the simulation study and the real data example show that the LTS has better pre- diction performance than its competitors in the presence of leverage points.
Keywords: breakdown point, outliers, penalized regression, robust regression, trimming
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