Robust estimates of the covariance matrix when there are missing data

VÍCTOR J. YOHAI; RUBÉN ZAMAR

Praga

Conferencia; International Conference on Robust Statistics (ICORS); 2010

Charles University in Prague

Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S-estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data, except for the obviously inefficient approach of deleting all incomplete cases. We generalize the definition of S-estimators of multivariate location and scatter to simultaneously deal with missing data and outliers. We show that the proposed estimators are strongly consistent under elliptical models when data are missing completely at random. We derive an EM type algorithm for computing the proposed estimators. This algorithm is initialized by an extension for missing data of the minimum volume ellipsoid. We asses the performance of our proposal by Monte Carlo simulation and give some real data examples.