A Bayesian non-parametric estimate for multivariate regression

The predictive approach to inference in multivariate regression problems is considered in a Bayesian non-parametric framework. A simple estimate of the regression coefficient matrix is derived under the Dirichlet process prior and then generalized by using a mixture of Dirichlet processes prior. These estimates are shown to belong to the class of linear Bayes estimates and their relation to ridge regression estimates is also exhibited. The paper ends with an illustrative application.