Abstract: In this paper, we propose an outlier detection procedure, based on a high-breakdown minimum ridge covariance determinant estimator that is especially useful for the large p/n scenario. The estimator is obtained from the subset of observations, after excluding potential outliers, by applying the so-called concentration steps. We explore the asymptotic distribution of the modified Mahalanobis distance related to the proposed estimator under certain moment conditions, and obtain a theoretical cutoff value for outlier identification. We also improve the outlier detection power by adding a one-step reweighting procedure. Lastly, we investigate the performance of the proposed methods using simulations and a real-data analysis.

Key words and phrases: High dimension, minimum covariance determinant estimator, random matrices.