Sparse least trimmed squares regression for analyzing high-dimensional large data sets

TL;DR

This paper introduces a robust and sparse regression method combining least trimmed squares with L1 penalty, effective for high-dimensional data with outliers, demonstrated on cancer gene expression data.

Contribution

It develops a novel sparse LTS estimator with a proven breakdown point and a fast algorithm, enhancing robustness and sparsity in high-dimensional regression.

Findings

Sparse LTS outperforms competitors in prediction accuracy with outliers.

The method effectively handles leverage points in high-dimensional data.

Application to cancer data demonstrates practical utility.

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.