EconStor >
Universität zu Köln >
Institut für Ökonometrie und Statistik, Universität Köln >
Discussion Papers in Econometrics and Statistics, Institut für Ökonometrie und Statistik, Universität Köln >

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10419/44947
  
Title:A generalization of Tyler's M-estimators to the case of incomplete data PDF Logo
Authors:Frahm, Gabriel
Jaekel, Uwe
Issue Date:2009
Series/Report no.:Discussion papers in statistics and econometrics 3/07
Abstract:Many different robust estimation approaches for the covariance or shape matrix of multivariate data have been established until today. Tyler's M-estimator has been recognized as the 'most robust' M-estimator for the shape matrix of elliptically symmetric distributed data. Tyler's Mestimators 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.
Subjects:covariance matrix
distribution-free estimation
missing data
robust estimation
shape matrix
sign-based estimator
Tyler's M-estimator
JEL:H12
H20
Document Type:Working Paper
Appears in Collections:Discussion Papers in Econometrics and Statistics, Institut für Ökonometrie und Statistik, Universität Köln

Files in This Item:
File Description SizeFormat
608698911.pdf580.56 kBAdobe PDF
No. of Downloads: Counter Stats
Download bibliographical data as: BibTeX
Share on:http://hdl.handle.net/10419/44947

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.