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

Anelia Somekh-Baruch, Amir Leshem, Venkatesh Saligrama

Research output: Contribution to journalArticlepeer-review

8 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 languageAmerican English
Pages (from-to)5549-5554
Number of pages6
JournalIEEE Transactions on Information Theory
Volume64
Issue number8
DOIs
StatePublished - Aug 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

  • Cramer-rao bound
  • constrained estimators
  • estimation theory
  • unbiased estimation

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