Estimating covariance matrices II

Wei-Liem Loh

Journal of Multivariate Analysis, 1991, vol. 36, issue 2, 163-174

Abstract: Let S1 and S2 be two independent p - p Wishart matrices with S1 ~ Wp([Sigma]1, n1) and S2 ~ Wp([Sigma]2, n2). We wish to estimate [zeta] = [Sigma]2[Sigma]1-1 under the loss function L1 = tr([zeta] - [zeta])' [Sigma]2-1([zeta] - [zeta]) [Sigma]1/tr [zeta]. By extending the techniques of Berger, Haff, and Stein for the one sample problem, alternative estimators to the usual estimators for [zeta] are obtained. However, the risks of these estimators are not available in closed form. A Monte Carlo study is used instead to evaluate their risk performances. The results indicate that the alternative estimators have excellent risk properties with respect to the usual estimators. In particular, dramatic savings in risk are obtained when the eigenvalues of [Sigma]2[Sigma]1-1 are close together.

Keywords: covariance; matrices; equivariant; estimation; unbiased; estimate; of; risk; Wishart; distribution (search for similar items in EconPapers)
Date: 1991
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(91)90055-7
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:36:y:1991:i:2:p:163-174

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().