A risk-unbiased approach to a new Cramér-Rao bound

Shahar Bar, Joseph Tabrikian

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

How accurately can one estimate a deterministic parameter subject to other unknown deterministic model parameters? The most popular answer to this question is given by the Cramer-Rao bound (CRB). The main assumption behind the derivation of the CRB is local unbiased estimation of all model parameters. The foundations of this work rely on doubting this assumption. Each parameter in its turn is treated as a single parameter of interest, while the other model parameters are treated as nuisance, as their mis-knowledge interferes with the estimation of the parameter of interest. Correspondingly, a new Cramer-Rao-type bound on the mean squared error (MSE) of non-Bayesian estimators is established with no unbiasedness condition on the nuisance parameters. Alternatively, Lehmann's concept of unbiasedness is imposed for a risk that measures the distance between the estimator and the locally best unbiased (LBU) estimator which assumes perfect knowledge of the nuisance parameters. The proposed bound is compared to the CRB and MSE of the maximum likelihood estimator (MLE). Simulations show that the proposed bound provides a tight lower bound for this estimator, compared with the CRB.

Original languageEnglish
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2921-2925
Number of pages5
ISBN (Electronic)9781479999880
DOIs
StatePublished - 18 May 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: 20 Mar 201625 Mar 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Conference

Conference41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Country/TerritoryChina
CityShanghai
Period20/03/1625/03/16

Keywords

  • Cramer-Rao bound
  • Lehmann unbiased-ness
  • MSE
  • nuisance parameters
  • risk-unbiasedness

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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