On the non-existence of unbiased estimators in constrained estimation problems
Files
Accepted manuscript
Date
2018-08-01
DOI
Authors
Saligrama, Venkatesh
Somekh-Baruch, Anelia
Lesham, Amir
Version
Accepted manuscript
OA Version
Citation
V. Saligrama, Anelia Somekh-Baruch, Amir Lesham. 2018. "On the Non-Existence of Unbiased Estimators in Constrained Estimation Problems." IEEE Transactions on Information 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.