Robust shrinkage estimation for elliptically symmetric distributions with unknown covariance matrix

✍ Scribed by Dominique Fourdrinier; William E. Strawderman; Martin T. Wells

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 198 KB
• Volume: 85
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1016/s0047-259x(02)00023-4

✦ Synopsis

Let X ; V 1 ; y; V nÀ1 be n random vectors in R p with joint density of the form

where both y and S are unknown. We consider the problem of the estimation of y with the invariant loss ðd À yÞ 0 S À1 ðd À yÞ and propose estimators which dominate the usual estimator d 0 ðX Þ ¼ X simultaneously for the entire class of such distributions. The proof involves the development of expressions which are analogous to unbiased estimators of risk and which in fact reduce to unbiased estimators of risk in the normal case. The method is applicable to the case where S is structured. As an example, we examine the case where S is diagonal.