A generalization of Tyler's M-estimators to the case of incomplete data

Many different robust estimation approaches for the covariance or shape matrix of multivariate data have been established. Tyler’s M-estimator has been recognized as the ‘most robust’ M-estimator for the shape matrix of elliptically symmetric distributed data. Tyler’s M-estimators for location and shape are generalized by taking account of incomplete data. It is shown that the shape matrix estimator remains distributionfree under the class of generalized elliptical distributions. Its asymptotic distribution is also derived and a fast algorithm, which works well even for high-dimensional data, is presented. A simulation study with clean and contaminated data covers the complete-data aswell as the incomplete-data case, where themissing data are assumed to beMCAR,MAR, and NMAR. © 2009 Elsevier B.V. All rights reserved.