NDLI: Bayesian Estimation in the Presence of Deterministic Nuisance Parameters

Content Provider	IEEE Xplore Digital Library
Author	Bar, S. Tabrikian, J.
Copyright Year	1991
Abstract	How accurately can one estimate a random parameter subject to unknown deterministic nuisance parameters? The hybrid Cramér-Rao bound (HCRB) provides an answer to this question for a restricted class of estimators. The HCRB is the most popular performance bound on the mean-square-error (MSE) for random parameter estimation problems which involve deterministic parameters. The HCRB is useful when one is interested in both the random and the deterministic parameters and in the coupling between their estimation errors. This bound refers to locally weak-sense unbiased estimators with respect to (w.r.t.) the deterministic parameters. However, if these parameters are nuisance, it is unnecessary to restrict their estimation as unbiased. This paper is the first of a two-part study of Bayesian parameter estimation in the presence of deterministic nuisance parameters. It begins with a study on order relations between existing Cramér-Rao (CR)-type bounds of mean-unbiased Bayesian estimators. Then, a new CR-type bound is developed with no assumption of unbiasedness on the nuisance parameters. Alternatively, Lehmann's concept of unbiasedness is employed rather than conventional mean-unbiasedness. It is imposed on a risk that measures the distance between the estimator and the minimum MSE (MMSE) estimator which assumes perfect knowledge of the nuisance parameters. In the succeeding paper, asymptotic performances of some Bayesian estimators with maximum likelihood based estimates for the nuisance parameters are investigated. The proposed risk-unbiased bound (RUB) is proved to be asymptotically achieved by the MMSE estimator with maximum likelihood estimates for the nuisance parameters, while the existing CR-type bounds are not necessarily achievable.
Sponsorship	IEEE Signal Processing Society
Starting Page	6632
Ending Page	6646
Page Count	15
File Size	4761965
File Format	PDF
ISSN	1053587X
Volume Number	63
Issue Number	24
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Bayes methods Parameter estimation Niobium Estimation error Probability density function Q measurement risk-unbiasedness Bayesian Cramér-Rao bound Bayesian estimation hybrid Cramér-Rao bound Lehmann-unbiasedness mean-square-error (MSE) nuisance parameters performance bounds
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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