Efficient shrinkage in parametric models

This paper introduces shrinkage for general parametric models. We show how to shrink maximum likelihood estimators towards parameter subspaces de…ned by general nonlinear restrictions. We derive the asymptotic distribution and risk of the generalized shrinkage estimator using a local asymptotic framework. We show that if the shrinkage dimension exceeds two, the asymptotic risk of the shrinkage estimator is strictly less than that of the MLE. This reduction holds globally in the parameter space. We show that the reduction in asymptotic risk is substantial, even for moderately large values of the parameters. The formula simplify in a very convenient way in the context of high dimensional models. We derive a simple bound for the asymptotic risk. We also provide a new large sample minimax e¢ ciency bound. We use the concept of local asymptotic minimax bounds, a generalization of the conventional asymptotic minimax bounds. The