New observations on efficiency of variance estimation of white Gaussian signal with unknown mean

Shahar Bar, Joseph Tabrikian

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

2 Scopus citations

Abstract

The uniformly minimum variance unbiased estimator (UMVUE) for mean and variance of white Gaussian noise is known to be not efficient. This is due to the fact that according to the Cramér-Rao bound (CRB), no coupling exists between mean and variance of Gaussian observations, while it is clear that knowledge or lack of knowledge of the mean has impact on estimation of the variance. In this work, we consider the problem of variance estimation in the presence of unknown mean of white Gaussian signals, where the unknown mean is considered to be a nuisance parameter. For this purpose, a Cramér-Rao-type bound on the mean-squared-error (MSE) of non-Bayesian estimators, which has been recently introduced, is analyzed. This bound considers 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 estimator, which assumes perfect knowledge of the model parameters. It is analytically shown that the MSE of the well-known UMVUE coincides with the proposed risk-unbiased CRB, and therefore it is called risk-efficient estimator.

Original languageEnglish
Title of host publication2016 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2016
PublisherIEEE Computer Society
ISBN (Electronic)9781509021031
DOIs
StatePublished - 15 Sep 2016
Event2016 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2016 - Rio de Rio de Janeiro, Brazil
Duration: 10 Jul 201613 Jul 2016

Publication series

NameProceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
Volume2016-September
ISSN (Electronic)2151-870X

Conference

Conference2016 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2016
Country/TerritoryBrazil
CityRio de Rio de Janeiro
Period10/07/1613/07/16

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