Uniformly best biased estimators in non-bayesian parameter estimation

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9 Scopus citations

Abstract

In this paper, a new structured approach for obtaining uniformly best non-Bayesian biased estimators, which attain minimum-mean-square-error performance at any point in the parameter space, is established. We show that if a uniformly best biased (UBB) estimator exists, then it is unique, and it can be directly obtained from any locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived. It is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and its closed-form expression is obtained. The proposed approach is exemplified in two nonlinear estimation problems, where uniformly minimum-variance-unbiased estimators do not exist. In the considered examples, we show that the UBB estimators outperform the corresponding maximum-likelihood estimators in the MSE sense.

Original languageEnglish
Article number5893945
Pages (from-to)7635-7647
Number of pages13
JournalIEEE Transactions on Information Theory
Volume57
Issue number11
DOIs
StatePublished - 1 Nov 2011

Keywords

  • Locally best biased (LBB) estimators
  • minimum-mean-square-error (MMSE)
  • non-Bayesian theory
  • parameter estimation
  • uniformly best biased (UBB) estimators

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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