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Empirical MSE Minimization to Estimate a Scalar Parameter

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arxiv 2006.14667 v1 pith:G6DIERTV submitted 2020-06-25 math.ST econ.EMstat.TH

Clément de Chaisemartin , Xavier D'Haultf{oe}uille This is my paper · ORCID
classification math.STecon.EMstat.TH
keywords estimatorsconsistentestimatorfirstmaximumotherparameterscalar
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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.

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