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 distribution-free 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 as well as the incomplete-data case, where the missing data are assumed to be MCAR, MAR, and NMAR.
Year of publication: |
2010
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Authors: | Frahm, Gabriel ; Jaekel, Uwe |
Published in: |
Computational Statistics & Data Analysis. - Elsevier, ISSN 0167-9473. - Vol. 54.2010, 2, p. 374-393
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Publisher: |
Elsevier |
Saved in:
Online Resource
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