Estimating multivariate random effects without replication
This paper considers the estimation of multivariate random effects that are measured with error, but for which there are no replications. Using structural simplification of the correlation of the data, separate estimates are generated for the covariance of the random effects and the covariance of the error. An estimator of the random effects based on a truncated eigen structure is defined, and matrix mean squared error and its trace (risk) are analyzed, with comparison to the maximum likelihood estimator (m.l.e) and also to the Stein-like estimator of Efron and Morris (1972). It is shown that the estimator has risk which is smaller than the risk of the maximum likelihood estimator and the Efron-Morris estimator in most cases.