Outlier Detection via a Minimum Ridge Covariance Determinant Estimator

In this paper, we propose an outlier detection procedure based on a high-breakdown minimum ridge covariance determinant estimator, which is especially 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 theoretical cut-off value for outlier identification.We achieve a further improvement on the outlier detection power by adding a one-step reweighting procedure.We investigate the performance of the proposed methods by simulations and a real data analysis.