The shrinkage approach in the combination of forecasts

An unbiased point estimator T for an unknown parameter θ can be improved in the sense of the Mean Squared Error (MSE) by T = λT λ for suitable factors λ. Here, we want to discuss this approach in the context of combination of forecasts. We consider the shrinkage technique for unbiased univariate and multivariate forecast combinations. In the univariate case our aim is to reduce the MSE. In the multivariate case we want to improve unbiased forecast combinations in the sense of the Scalar Mean Squared Error (SMSE) or the Matrix Mean Squared Error (MMSE).