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Empirical MSE Minimization to Estimate a Scalar Parameter

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  • Cl'ement de Chaisemartin
  • Xavier D'Haultf{oe}uille

Abstract

We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an assumption is satisfied. We propose to use the weighted sum of the two estimators with the lowest estimated mean-squared error (MSE). We show that this third estimator dominates the other two from a minimax-regret perspective: the maximum asymptotic-MSE-gain one may incur by using this estimator rather than one of the other estimators is larger than the maximum asymptotic-MSE-loss.

Suggested Citation

  • Cl'ement de Chaisemartin & Xavier D'Haultf{oe}uille, 2020. "Empirical MSE Minimization to Estimate a Scalar Parameter," Papers 2006.14667, arXiv.org.
    • Handle: RePEc:arx:papers:2006.14667
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    References listed on IDEAS

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    3. Judge G.G. & Mittelhammer R.C., 2004. "A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 479-487, January.
    4. Breusch, Trevor & Ward, Michael B. & Nguyen, Hoa Thi Minh & Kompas, Tom, 2011. "On the Fixed-Effects Vector Decomposition," Political Analysis, Cambridge University Press, vol. 19(2), pages 123-134, April.
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    Cited by:

    1. Aristotelis Epanomeritakis & Davide Viviano, 2025. "Learning What to Learn: Experimental Design when Combining Experimental with Observational Evidence," Papers 2510.23434, arXiv.org, revised Dec 2025.

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