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

Statistics Theory 2016-09-26 v1 Information Theory math.IT Statistics Theory

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.

Keywords

Cite

@article{arxiv.1609.07415,
  title  = {On the Non-Existence of Unbiased Estimators in Constrained Estimation Problems},
  author = {Anelia Somekh-Baruch and Amir Leshem and Venkatesh Saligrama},
  journal= {arXiv preprint arXiv:1609.07415},
  year   = {2016}
}