Improved estimation of a patterned covariance matrix

Dipak K. Dey and Alan E. Gelfand

Journal of Multivariate Analysis, 1989, vol. 31, issue 1, 107-116

Abstract: Suppose a random vector X has a multinormal distribution with covariance matrix [Sigma] of the form [Sigma] = [Sigma]i=1k [theta]iMi, where Mi's form a known complete orthogonal set and [theta]i's are the distinct unknown eigenvalues of [Sigma]. The problem of estimation of [Sigma] is considered under several plausible loss functions. The approach is to establish a duality relationship: estimation of the patterned covariance matrix [Sigma] is dual to simulataneous estimation of scale parameters of independent [chi]2 distributions. This duality allows simple estimators which, for example, improve upon the MLE of [Sigma]. It also allows improved estimation of tr [Sigma]. Examples are given in the case when [Sigma] has equicorrelated structure.

Keywords: patterned; covariance; matrix; loss; function; simultaneous; estimation; equicorrelated; model (search for similar items in EconPapers)
Date: 1989
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