Abstract

Estimating the location and scatter of multivariate data is a first step in multivariate statistical analyses. Often, the resulting scatter matrix needs to be non-singular, which is for example not the case when there are more variables than observations. Regularization techniques are then necessary; they usually consist of penalizing the likelihood function, and are sensitive to contamination in the data. In this talk, a robust regularization covariance matrix estimator will be proposed and discussed. We show its breakdown point and discuss algorithms for computation. The talk will consider several applications: (i) Outlier detection in high dimensional data settings (ii) robust graphical modeling (iii) robust and sparse regression.