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dc.contributor.authorFrahm, Gabrielen_US
dc.description.abstractIt 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.en_US
dc.publisherUniv., Seminar für Wirtschafts- und Sozialstatistik Kölnen_US
dc.relation.ispartofseriesDiscussion papers in statistics and econometrics 5/07en_US
dc.subject.keywordlocal asymptotic normalityen_US
dc.subject.keywordrobust covariance matrix estimatoren_US
dc.subject.keywordscale-invariant functionen_US
dc.subject.keywordshape matrixen_US
dc.subject.keywordTyler's M-estimatoren_US
dc.titleAsymptotic distributions of robust shape matrices and scalesen_US
dc.typeWorking Paperen_US
Appears in Collections:Discussion Papers in Econometrics and Statistics, Institut für Ökonometrie und Statistik, Universität Köln

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