On combining unbiased and possibly biased correlated estimators

We study estimators that combine an unbiased estimator with a possibly biased correlated estimator of a mean vector. The combined estimators are shrinkage-type estimators that shrink the unbiased estimator towards the biased estimator. Conditions under which the combined estimator dominates the original unbiased estimator are given. Models studied include normal models with a known covariance structure, scale mixtures of normals, and more generally elliptically symmetric models with a known covariance structure. Elliptically symmetric models with a covariance structure known up to a multiple are also considered.