On the Non-Existence of Unbiased Estimators in Constrained Estimation Problems

Anelia Somekh-Baruch; Amir Leshem; Venkatesh Saligrama

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arXiv · 1609.07415

On the Non-Existence of Unbiased Estimators in Constrained Estimation Problems

Anelia Somekh-Baruch·Amir Leshem·Venkatesh Saligrama

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Abstract

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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BibTeX RIS

Anelia Somekh-Baruch, Amir Leshem, Venkatesh Saligrama. 2016-09-23. On the Non-Existence of Unbiased Estimators in Constrained Estimation Problems. https://arxiv.org/abs/1609.07415

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