On multivariate ridge regression

A multivariate linear regression model with q responses as a linear function ofpindependent variables ry,= + k is considered withapxqparameter matrix B. The least squares (or Maximum Likelihood for multivariate normal E) % % estimator of B is deficient in that it takes no account of the % "across regression" correlations, on the one hand, and ignores the famous Stein effect, on the other hand. A remedy was offered by Brown and 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 and Zidek multivariate ridge estimators., Efron and Morris' estimators of several normal mean vectors and Fearn's Bayesian estimators of growth curves as special cases. The unknown covariance cases result in an identifiability problem which is treated in a Bayesian fashion using conjugate priors. The method is then applied to forecasting the final election results from partial returns obtained at election night.