B1320
Title: Robust and sparse estimation in multivariate statistics
Authors: Christophe Croux - Leuven (Belgium) [presenting]
Abstract: Sparse and robust estimation methods for multivariate statistics are presented. The lasso is the most popular sparse estimator for linear regression. However, it is not robust, and its breakdown point can be shown to be zero. One of the first robust alternatives for the lasso is the Sparse Least Trimmed Squares estimator. The advantage of the latter estimator is that it can be computed without the need for an initial robust sparse estimator. Moreover, it is operational and available as an R-package. We go beyond the regression model: (i) We show how a robust and sparse version of the Minimum Covariance Determinant covariance matrix estimator can be attained (ii) We give an approaches to robust and sparse principal component analysis (iii) We present a robust and sparse version of Canonical Correlation Analysis. We elaborate on the robust and sparse canonical correlation method, and show its good performance on several real data examples.
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