NDLI: Shrinkage Algorithms for MMSE Covariance Estimation

Content Provider	IEEE Xplore Digital Library
Author	Yilun Chen Wiesel, A. Eldar, Y.C. Hero, A.O.
Copyright Year	1991
Abstract	We address covariance estimation in the sense of minimum mean-squared error (MMSE) when the samples are Gaussian distributed. Specifically, we consider shrinkage methods which are suitable for high dimensional problems with a small number of samples (large p small n). First, we improve on the Ledoit-Wolf (LW) method by conditioning on a sufficient statistic. By the Rao-Blackwell theorem, this yields a new estimator called RBLW, whose mean-squared error dominates that of LW for Gaussian variables. Second, to further reduce the estimation error, we propose an iterative approach which approximates the clairvoyant shrinkage estimator. Convergence of this iterative method is established and a closed form expression for the limit is determined, which is referred to as the oracle approximating shrinkage (OAS) estimator. Both RBLW and OAS estimators have simple expressions and are easily implemented. Although the two methods are developed from different perspectives, their structure is identical up to specified constants. The RBLW estimator provably dominates the LW method for Gaussian samples. Numerical simulations demonstrate that the OAS approach can perform even better than RBLW, especially when n is much less than p . We also demonstrate the performance of these techniques in the context of adaptive beamforming.
Sponsorship	IEEE Signal Processing Society
Starting Page	5016
Ending Page	5029
Page Count	14
File Size	1365945
File Format	PDF
ISSN	1053587X
Volume Number	58
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Array signal processing Covariance matrix Ambient intelligence Iterative methods Permission Computer science Iron Statistics Yield estimation Estimation error shrinkage Beamforming covariance estimation minimum mean-squared error (MMSE)
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

Shrinkage-to-Tapering Estimation of Large Covariance Matrices

Multi-Target Shrinkage Estimation for Covariance Matrices

Robust Adaptive Beamforming Using a Low-Complexity Shrinkage-Based Mismatch Estimation Algorithm

Covariance Matrix Estimation With Heterogeneous Samples

Regularized Covariance Matrix Estimation via Empirical Bayes

Minimax estimation of deterministic parameters in linear models with a random model matrix

A Competitive Mean-Squared Error Approach to Beamforming

On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary

A Bayesian Robust Adaptive Beamforming Based on Phase-Invariant MMSE Criterion

Shrinkage Algorithms for MMSE Covariance Estimation

Similar Documents

Shrinkage-to-Tapering Estimation of Large Covariance Matrices

Multi-Target Shrinkage Estimation for Covariance Matrices

Robust Adaptive Beamforming Using a Low-Complexity Shrinkage-Based Mismatch Estimation Algorithm

Covariance Matrix Estimation With Heterogeneous Samples

Regularized Covariance Matrix Estimation via Empirical Bayes

Minimax estimation of deterministic parameters in linear models with a random model matrix

A Competitive Mean-Squared Error Approach to Beamforming

On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary

A Bayesian Robust Adaptive Beamforming Based on Phase-Invariant MMSE Criterion

Shrinkage Algorithms for MMSE Covariance Estimation