On a Conjecture of Krishnamoorthy and Gupta,
AbstractWe consider the problem of estimating the precision matrix ([Sigma]-1) under a fully invariant convex loss. Suppose that there exists a minimax constant risk estimator[Phi](say) for this problem. K. Krishnamoorthy and A. K. Gupta have proposed an operation which transforms this estimator into an orthogonally invariant estimator[Phi]* (say) and they have a conjecture saying that[Phi]* is minimax as well. This paper contains two parts. In the first part, we present counterexamples. In the second part, we elaborate a technique which can be used to prove that certain estimators are minimax. This technique is then applied successfully to some of the estimators proposed in the Krishnamoorthy and Gupta paper.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 62 (1997)
Issue (Month): 1 (July)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
- Perron, F., 1992. "Minimax estimators of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 16-28, October.
- Sheena, Yo & Takemura, Akimichi, 1992. "Inadmissibility of non-order-preserving orthogonally invariant estimators of the covariance matrix in the case of Stein's loss," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 117-131, April.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.