Asymptotic distributions of robust shape matrices and scales
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.
|Date of creation:||2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 0221 / 470 5607
Fax: 0221 / 470 5179
Web page: http://www.wisostat.uni-koeln.de/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:zbw:ucdpse:507. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics)
If references are entirely missing, you can add them using this form.