Estimating the covariance matrix: a new approach

✍ Scribed by T. Kubokawa; M.S. Srivastava

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 242 KB
• Volume: 86
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1016/s0047-259x(02)00053-2

✦ Synopsis

In this paper, we consider the problem of estimating the covariance matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean. A new method is presented to obtain a truncated estimator that utilizes the information available in the sample mean matrix and dominates the James-Stein minimax estimator. Several scale equivariant minimax estimators are also given. This method is then applied to obtain new truncated and improved estimators of the generalized variance; it also provides a new proof to the results of Shorrock and Zidek (Ann. Statist. 4 (1976) 629) and Sinha (J. Multivariate Anal. 6 (1976) 617).