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.
Bibliographical noteFunding Information:
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.
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- Cramer-rao bound
- constrained estimators
- estimation theory
- unbiased estimation