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Combining least-squares regressions: an upper-bound on mean-squared error

For Gaussian regression, we develop and analyse methods for combining estimators from various models. For squared-error loss, an unbiased estimator of the risk of a mixture of general estimators is developed. Special attention is given to the case that the components are least-squares projections into arbitrary linear subspaces. We relate the unbiased risk estimate for the mixture estimator to estimates of the risks achieved by the components. This results in accurate bounds on the risk and its unbiased estimate - without advance knowledge of which model is best, the resulting performance is comparable to what is achieved by the best of the individual models