Achievable MSE lower bounds in non-bayesian biased estimation

Koby Todros; Joseph Tabrikian

doi:10.1109/SAM.2010.5606710

Achievable MSE lower bounds in non-bayesian biased estimation

Koby Todros, Joseph Tabrikian

Department of Electrical & Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

In this paper, a new structured approach for obtaining uniformly best biased (UBB) estimators, in the mean-square-error (MSE) sense, is established. We show that if a UBB estimator exists, then it is uniquely given by the locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived, and it is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and the UBB estimator is directly obtained from the LBB estimator. The UBB estimator is derived in a non-linear Gaussian estimation problem. In comparison to the maximum-likelihood estimator, we show that the UBB estimator exhibits superior estimation performance in the MSE sense.

Original language	English
Title of host publication	2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010
Pages	117-120
Number of pages	4
DOIs	https://doi.org/10.1109/SAM.2010.5606710
State	Published - 20 Dec 2010
Event	2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010 - Jerusalem, Israel Duration: 4 Oct 2010 → 7 Oct 2010

Publication series

Name	2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010

Conference

Conference	2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010
Country/Territory	Israel
City	Jerusalem
Period	4/10/10 → 7/10/10

Keywords

Locally best biased estimators
MMSE estimation
Non-Bayesian estimation
Parameter estimation
Uniformly best biased estimators

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

Access to Document

10.1109/SAM.2010.5606710

Cite this

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title = "Achievable MSE lower bounds in non-bayesian biased estimation",

abstract = "In this paper, a new structured approach for obtaining uniformly best biased (UBB) estimators, in the mean-square-error (MSE) sense, is established. We show that if a UBB estimator exists, then it is uniquely given by the locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived, and it is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and the UBB estimator is directly obtained from the LBB estimator. The UBB estimator is derived in a non-linear Gaussian estimation problem. In comparison to the maximum-likelihood estimator, we show that the UBB estimator exhibits superior estimation performance in the MSE sense.",

keywords = "Locally best biased estimators, MMSE estimation, Non-Bayesian estimation, Parameter estimation, Uniformly best biased estimators",

author = "Koby Todros and Joseph Tabrikian",

year = "2010",

month = dec,

day = "20",

doi = "10.1109/SAM.2010.5606710",

language = "English",

isbn = "9781424489770",

series = "2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010",

pages = "117--120",

booktitle = "2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010",

note = "2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010 ; Conference date: 04-10-2010 Through 07-10-2010",

}

Todros, K & Tabrikian, J 2010, Achievable MSE lower bounds in non-bayesian biased estimation. in 2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010., 5606710, 2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010, pp. 117-120, 2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010, Jerusalem, Israel, 4/10/10. https://doi.org/10.1109/SAM.2010.5606710

Achievable MSE lower bounds in non-bayesian biased estimation. / Todros, Koby ; Tabrikian, Joseph.
2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010. 2010. p. 117-120 5606710 (2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this paper, a new structured approach for obtaining uniformly best biased (UBB) estimators, in the mean-square-error (MSE) sense, is established. We show that if a UBB estimator exists, then it is uniquely given by the locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived, and it is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and the UBB estimator is directly obtained from the LBB estimator. The UBB estimator is derived in a non-linear Gaussian estimation problem. In comparison to the maximum-likelihood estimator, we show that the UBB estimator exhibits superior estimation performance in the MSE sense.

AB - In this paper, a new structured approach for obtaining uniformly best biased (UBB) estimators, in the mean-square-error (MSE) sense, is established. We show that if a UBB estimator exists, then it is uniquely given by the locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived, and it is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and the UBB estimator is directly obtained from the LBB estimator. The UBB estimator is derived in a non-linear Gaussian estimation problem. In comparison to the maximum-likelihood estimator, we show that the UBB estimator exhibits superior estimation performance in the MSE sense.

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Achievable MSE lower bounds in non-bayesian biased estimation

Abstract

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Conference

Keywords

ASJC Scopus subject areas

Access to Document

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