The Annals of Statistics

Estimation of a Covariance Matrix under Stein's Loss

Dipak K. Dey and C. Srinivasan

Full-text: Open access

Abstract

Stein's general technique for improving upon the best invariant unbiased and minimax estimators of the normal covariance matrix is described. The technique is to obtain solutions to a certain differential inequality involving the eigenvalues of the sample covariance matrix. Several improved estimators are obtained by solving the differential inequality. These estimators shrink or expand the sample eigenvalues depending on their magnitude. A scale invariant, adaptive minimax estimator is also obtained.

Article information

Source
Ann. Statist., Volume 13, Number 4 (1985), 1581-1591.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349756

Digital Object Identifier
doi:10.1214/aos/1176349756

Mathematical Reviews number (MathSciNet)
MR811511

Zentralblatt MATH identifier
0582.62042

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 62C99: None of the above, but in this section

Keywords
Covariance matrix Wishart distribution Stein's loss orthogonally invariant estimators minimax estimators

Citation

Dey, Dipak K.; Srinivasan, C. Estimation of a Covariance Matrix under Stein's Loss. Ann. Statist. 13 (1985), no. 4, 1581--1591. doi:10.1214/aos/1176349756. https://projecteuclid.org/euclid.aos/1176349756


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