NDLI: MSE Bounds With Affine Bias Dominating the CramÉr

Content Provider	IEEE Xplore Digital Library
Author	Eldar, Y.C.
Copyright Year	1991
Abstract	In continuation to an earlier work, we further develop bounds on the mean-squared error (MSE) when estimating a deterministic parameter vector thetas₀ in a given estimation problem, as well as estimators that achieve the optimal performance. The traditional Cramer-Rao (CR) type bounds provide benchmarks on the variance of any estimator of thetas₀ under suitable regularity conditions, while requiring a priori specification of a desired bias gradient. To circumvent the need to choose the bias, which is impractical in many applications, it was suggested in our earlier work to directly treat the MSE, which is the sum of the variance and the squared-norm of the bias. While previously we developed MSE bounds assuming a linear bias vector, here we study, in the same spirit, affine bias vectors. We demonstrate through several examples that allowing for an affine transformation can often improve the performance significantly over a linear approach. Using convex optimization tools we show that in many cases we can choose an affine bias that results in an MSE bound that is smaller than the unbiased CR bound for all values of thetas₀. Furthermore, we explicitly construct estimators that achieve these bounds in cases where an efficient estimator exists, by performing an affine transformation of the standard maximum likelihood (ML) estimator. This leads to estimators that result in a smaller MSE than ML for all possible values of thetas₀.
Sponsorship	IEEE Signal Processing Society
Starting Page	3824
Ending Page	3836
Page Count	13
File Size	866016
File Format	PDF
ISSN	1053587X
Volume Number	56
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-08-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Maximum likelihood estimation Vectors Chromium Parameter estimation Minimax techniques Density measurement Probability density function Wireless communication Estimation error minimax bounds Affine bias biased estimation CramÉr–Rao bound (CRB) dominating estimators maximum likelihood mean-squared error (MSE) bounds
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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