A note on covariance estimation in the unbiased estimator of risk framework
Bala Rajaratnam,Dario Vincenzi +1 more
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In this paper, the authors leverage Stein's unbiased estimator of risk framework to obtain a proof-of-concept for constructing covariance estimators which retain the attractive properties of Stein's estimator and are simultaneously better than the MLE.About:
This article is published in Journal of Statistical Planning and Inference.The article was published on 2016-08-01 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Stein's unbiased risk estimate & Minimum-variance unbiased estimator.read more
Citations
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Journal ArticleDOI
A theoretical study of Stein's covariance estimator
Bala Rajaratnam,Dario Vincenzi +1 more
TL;DR: In this paper, an analysis of Stein's covariance estimator within the unbiased estimator of risk (UBEOR) framework is presented, which leads to important theoretical and methodological insights that are relevant for applications.
Journal ArticleDOI
Quadratic shrinkage for large covariance matrices
TL;DR: In this article , the authors proposed a new estimator for large covariance matrices by drawing a bridge between the classic (Stein (1975)) estimator in finite samples and recent progress under large-dimensional asymptotics.
Properties and use ofC M B power spectrum likelihoods
TL;DR: In this paper, the optimality of hybrid pseudo-C{sub l} cosmic microwave background power spectrum estimators and their covariances is investigated, and the number of samples required to estimate the covariance from simulations, with and without a good analytic approximation, is assessed.
ReportDOI
Sample-Starved Large Scale Network Analysis
Alfred O. Hero,Bala Rajaratnam +1 more
TL;DR: This research project developed correlation mining methods to answer the following fundamental question about complex networks: What are the fundamental limits on the amount of information that can be inferred about a network from a small number n of indirect empirical observations?
Book ChapterDOI
On Parameter Estimation for High Dimensional Errors-in-Variables Models
Silvelyn Zwanzig,Rauf Ahmad +1 more
TL;DR: In this paper, the estimation of parameter vector for a linear model with errors-in-variables is considered when the number of regressors may exceed the sample size, and new approaches are assessed.
References
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Journal ArticleDOI
A well-conditioned estimator for large-dimensional covariance matrices
Olivier Ledoit,Michael Wolf +1 more
TL;DR: This paper introduces an estimator that is both well-conditioned and more accurate than the sample covariance matrix asymptotically, that is distribution-free and has a simple explicit formula that is easy to compute and interpret.
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A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics
TL;DR: This work proposes a novel shrinkage covariance estimator that exploits the Ledoit-Wolf (2003) lemma for analytic calculation of the optimal shrinkage intensity and applies it to the problem of inferring large-scale gene association networks.
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Honey, I shrunk the sample covariance matrix
Olivier Ledoit,Michael Wolf +1 more
TL;DR: Shrinkage as mentioned in this paper is a matrix obtained from the sample covariance matrix through a transformation called shrinkage, which pulls the most extreme coefficients toward more central values, systematically reducing estimation error when it matters most.
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Estimation of a Covariance Matrix Using the Reference Prior
Ruo-Yong Yang,James O. Berger +1 more
TL;DR: In this paper, a non-informative prior for a covariance matrix was developed from a Bayesian perspective, and expressions for the resulting Bayes estimators were derived using the hit-and-run sampler.
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Empirical Bayes Estimation of the Multivariate Normal Covariance Matrix
TL;DR: In this article, the authors show that the uniform reduction in the risk function determined by the empirical Bayes estimator is at least $100(p + 1)/(k + p + 1)+(k+p+1)+(n) + 1/k).