Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation

SUMMARY The detection of atypical observations from multivariate data sets can be enhanced by examining probabilityplotsofMahalanobis squared distances using robust M-estimates of means and of covariances, rather than the usual maximum likelihood estimates. The weights associated with the robust estimation can also be used to indicate atypical observations. For uncontaminated data, the robust estimates are similar to the usual estimates. A procedure for robust principal component analysis is given; it also indicates atypical observations and provides an analysis relatively little influenced by such observations.