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Efficient shrinkage in parametric models

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  • Hansen, Bruce E.

Abstract

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.

Suggested Citation

  • Hansen, Bruce E., 2016. "Efficient shrinkage in parametric models," Journal of Econometrics, Elsevier, vol. 190(1), pages 115-132.
    • Handle: RePEc:eee:econom:v:190:y:2016:i:1:p:115-132
    DOI: 10.1016/j.jeconom.2015.09.003
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    References listed on IDEAS

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    6. DiTraglia, Francis J., 2016. "Using invalid instruments on purpose: Focused moment selection and averaging for GMM," Journal of Econometrics, Elsevier, vol. 195(2), pages 187-208.
    7. Hansen, Bruce E., 2015. "Shrinkage Efficiency Bounds," Econometric Theory, Cambridge University Press, vol. 31(4), pages 860-879, August.
    8. Berger, James, 1976. "Minimax estimation of a multivariate normal mean under arbitrary quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 6(2), pages 256-264, June.
    9. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
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