EconStor >
Universität zu Köln >
Seminar für Wirtschafts- und Sozialstatistik, Universität Köln >
Discussion Papers in Statistics and Econometrics, Seminar für Wirtschafts- und Sozialstatistik, Universität Köln >

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

http://hdl.handle.net/10419/44943
  
Title:Asymptotic distributions of robust shape matrices and scales PDF Logo
Authors:Frahm, Gabriel
Issue Date:2008
Series/Report no.:Discussion papers in statistics and econometrics 5/07
Abstract:It has been frequently observed in the literature that many multivariate statistical methods require the covariance or dispersion matrix ∑ of an elliptical distribution only up to some scaling constant. If the topic of interest is not the scale but only the shape of the elliptical distribution, it is not meaningful to focus on the asymptotic distribution of an estimator for ∑ or another matrix Γ ∝ ∑. In the present work, robust estimators for the shape matrix and the associated scale are investigated. Explicit expressions for their joint asymptotic distributions are derived. It turns out that if the joint asymptotic distribution is normal, the presented estimators are asymptotically independent for one and only one specific choice of the scale function. If it is non-normal (this holds for example if the estimators for the shape matrix and scale are based on the minimum volume ellipsoid estimator) only the presented scale function leads to asymptotically uncorrelated estimators. This is a generalization of a result obtained by Paindaveine (2008) in the context of local asymptotic normality theory.
Subjects:local asymptotic normality
M-estimator
R-estimator
robust covariance matrix estimator
scale-invariant function
S-estimator
shape matrix
Tyler's M-estimator
JEL:H20
E20
Document Type:Working Paper
Appears in Collections:Discussion Papers in Statistics and Econometrics, Seminar für Wirtschafts- und Sozialstatistik, Universität Köln

Files in This Item:
File Description SizeFormat
608699551.pdf169.97 kBAdobe PDF
No. of Downloads: Counter Stats
Download bibliographical data as: BibTeX
Share on:http://hdl.handle.net/10419/44943

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