Improved estimation of a patterned covariance matrix

Suppose a random vector X has a multinormal distribution with covariance matrix Σ of the form Σ = Σi=1^k θiMi, where Mi's form a known complete orthogonal set and θi's are the distinct unknown eigenvalues of Σ. The problem of estimation of Σ is considered under several plausible loss functions. The approach is to establish a duality relationship: estimation of the patterned covariance matrix Σ is dual to simulataneous estimation of scale parameters of independent χ² distributions. This duality allows simple estimators which, for example, improve upon the MLE of Σ. It also allows improved estimation of tr Σ. Examples are given in the case when Σ has equicorrelated structure. © 1989.

Duke Scholars

Author Alan E. Gelfand Statistical Science