On the non-existence of unbiased estimators in constrained estimation problems
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Citation (published version)Anelia Somekh-Baruch, Amir Leshem, Venkatesh Saligrama. 2017. "On the Non-Existence of Unbiased Estimators in Constrained Estimation Problems." IEEE Transactions on Information Theory, pp. 1 - 1. https://doi.org/10.1109/TIT.2017.2731845
We address the problem of existence of unbiased constrained parameter estimators. We show that if the constrained set of parameters is compact and the hypothesized distributions are absolutely continuous with respect to one another, then there exists no unbiased estimator.Weaker conditions for the absence of unbiased constrained estimators are also specified. We provide several examples which demonstrate the utility of these conditions.
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