Optimal biased estimation using Lehmann-unbiasedness

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

Abstract

This paper deals with non-Bayesian parameter estimation under the mean-squared-error (MSE), which is a topic of great interest in various engineering fields. Although the unbiasedness condition is commonly used in non-Bayesian MSE estimation, in many cases biased estimation may result in better performance. However, no method for determining the optimal bias function in general cases is available. We propose a new approach for uniform minimum MSE biased estimation, where the optimal bias is chosen in accordance with Lehmann-unbiasedness definition. The proposed approach is based on modifying the MSE risk by its multiplication with a weighting function of the unknown parameter, g2. Under this modified risk, Lehmann's definition of unbiasedness provides a condition referred to as g-unbiasedness. By using the g-unbiasedness, we derive a novel Cramér-Rao-type lower bound on the MSE of locally g-unbiased estimators. In addition, we show that if there exists an estimator that achieves the new bound, then it is produced by the penalized maximum likelihood estimator with a penalty function log g. Simulations show that the proposed approach can lead to non-trivial estimators with lower MSE than existing mean-unbiased estimators.

Original languageEnglish
Title of host publication2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4496-4500
Number of pages5
ISBN (Electronic)9781509041176
DOIs
StatePublished - 16 Jun 2017
Event2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States
Duration: 5 Mar 20179 Mar 2017

Publication series

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

Conference

Conference2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Country/TerritoryUnited States
CityNew Orleans
Period5/03/179/03/17

Keywords

  • Cramér-Rao bound
  • Lehmann-unbiasedness
  • Non-Bayesian parameter estimation
  • mean-squared- error (MSE)
  • penalized maximum likelihood

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