This paper introduces shrinkage for general parametric models. We show how to shrink maximum likelihood estimators towards parameter subspaces defined by general nonlinear restrictions. We derive the asymptotic distribution and risk of our 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 maximum likelihood estimator (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.
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