On the non-existence of unbiased estimators in constrained estimation problems

Anelia Somekh-Baruch; Amir Leshem; Venkatesh Saligrama

doi:10.1109/TIT.2017.2731845

On the non-existence of unbiased estimators in constrained estimation problems

Anelia Somekh-Baruch
, Amir Leshem
, Venkatesh Saligrama

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Boston University

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English
Pages (from-to)	5549-5554
Number of pages	6
Journal	IEEE Transactions on Information Theory
Volume	64
Issue number	8
DOIs	https://doi.org/10.1109/TIT.2017.2731845
State	Published - Aug 2018

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Funding

Manuscript received September 23, 2016; revised March 25, 2017 and June 21, 2017; accepted July 6, 2017. Date of publication August 1, 2017; date of current version July 12, 2018. This work was supported in part by NSF under Grant CCF: 1320566, Grant CNS: 1330008, and Grant CCF: 1527618, in part by the U.S. Department of Homeland Security, Science and Technology Directorate, Office of University Programs, under Grant Award 2013-ST-061-ED0001, in part by ONR Grant 50202168 and in part the U.S. AF under Contract FA8650-14-C-1728. The work of A. Leshem was supported in part by the Visiting Scholar Program of Boston University and in part by the Israel Science Foundation under Grant 903/2013. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the social policies, either expressed or implied, of the NSF, U.S. DHS, ONR, or AF. This paper was presented in part at the 2017 Information Theory and Application Workshop.

Funders	Funder number
Office of University Programs	2013-ST-061-ED0001
U.S. AF	FA8650-14-C-1728
National Science Foundation	1330008, 1527618, 1320566
Office of Naval Research	50202168
U.S. Department of Homeland Security
Boston University
Science and Technology Directorate
Israel Science Foundation	903/2013

Keywords

Cramer-rao bound
constrained estimators
estimation theory
unbiased estimation

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10.1109/TIT.2017.2731845

Cite this

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On the non-existence of unbiased estimators in constrained estimation problems

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