Abstract
SUMMARY A multivariate linear regression model with q responses as a linear function of p independent variables is considered with a p x q parameter matrix B. The least-squares or normal-theory maximum likelihood estimate of B is deficient in that it takes no account of the 'across regression' correlations, and ignores the Stein effect. A remedy was offered by Brown & Zidek (1980) in the form of a multivariate ridge estimator. A richer class of estimators is obtained here by casting the model in a linear hierarchical framework, obtaining the Brown & Zidek multivariate ridge estimates, Efron & Morris's estimates of several normal mean vectors and Fearn's Bayesian estimates of growth curves as special cases. The unknown covariance case results in an identifiability problem, which can be overcome by a Bayesian approach using conjugate priors for the unidentified covariance matrices.
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