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We show that in a common high-dimensional covariance model, the choice of loss function has a profound effect on optimal estimation.
Normal multivariate analysis and the orthogonal group
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Charles Stein · 1956
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Jegadevan Balendran Selliah · 1964
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LR Haff · 1979
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LR Haff · 1979
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A limit theorem for the norm of random matrices
Stuart Geman · 1980
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Estimation in continuous exponential families: Bayesian estimation subject to risk restrictions and inadmissibility results
James Berger · 1982
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The distance between two random vectors with given dispersion matrices
Ingram Olkin and Friedrich Pukelsheim · 1982
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DC Dowson and BV Landau · 1982
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Dipak K Dey and C Srinivasan · 1985
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A monte carlo comparison of four estimators for a covariance matrix
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Lectures on the theory of estimation of many parameters
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Inadmissibility of the best equivariant estimators of the variance-covariance matrix, the precision matrix, and the generalized variance under entropy loss
BK Sinha and M. Ghosh · 1987
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Developments in eigenvalue estimation
Robb J Muirhead · 1987
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Improved estimation of a covariance matrix under quadratic loss
Tatsuya Kubokawa · 1989
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Improved minimax estimation of a normal precision matrix
K Krishnamoorthy and AK Gupta · 1989
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Improved minimax estimation of a normal precision matrix
K. Krishnamoorthy and A. K. Gupta · 1989
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Estimating the covariance matrix and the generalized variance under a symmetric loss
Tatsuya Kubokawa and Yoshihiko Konno · 1990
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Estimating covariance matrices
Wei-Liem Loh · 1991
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On estimation of a matrix of normal means with unknown covariance matrix
Yoshihiko Konno · 1991
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Estimating the normal dispersion matrix and the precision matrix from a decision-theoretic point of view: a review
N Pal · 1993
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High dimensional covariance matrix estimation using a factor model
Jianqing Fan, Yingying Fan, and Jinchi Lv · 2008
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Central limit theorems for eigenvalues in a spiked population model
Zhidong Bai and Jian-feng Yao · 2008
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Operator norm consistent estimation of large-dimensional sparse covariance matrices
Noureddine El Karoui · 2008
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Non-euclidean statistics for covariance matrices, with applications to diffusion tensor imaging
Ian L. Dryden, Alexey Koloydenko, and Diwei Zhou · 2009
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Non-parametric detection of the number of signals: Hypothesis testing and random matrix theory
Shira Kritchman and Boaz Nadler · 2009
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Estimation of a covariance matrix using the reference prior
Ruoyong Yang and James O Berger · 1994
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Minimax risk over ℓ p \ell_{p} -balls for ℓ p \ell_{p} -error
David L Donoho and Iain M Johnstone · 1994
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Improved minimax estimators of normal covariance and precision matrices
AK Gupta and Samuel Ofori-Nyarko · 1995
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Estimation of the multivariate normal precision and covariance matrices in a star-shape model
D. Sun and X. Sun · 1996
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On orthogonal and symplectic matrix ensembles
C. A. Tracy and H. Widom · 1996
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Matrix analysis
Rajendra Bhatia · 1997
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Lawrence D. Brown and Eitan Greenshtein · 2009
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Shrinkage algorithms for mmse covariance estimation
Yilun Chen, Ami Wiesel, Yonina C Eldar, and Alfred O Hero · 2010
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NIST Handbook of Mathematical Functions
F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, editors · 2010
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Spectral analysis of large dimensional random matrices
Zhidong Bai and Jack W Silverstein · 2010
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Eigenvectors of some large sample covariance matrix ensembles
Olivier Ledoit and Sandrine Péché · 2011
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The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices
Florent Benaych-Georges and Raj Rao Nadakuditi · 2011
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Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
F. Benaych-Georges, A. Guionnet, and M. Maida · 2011
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Nonlinear shrinkage estimation of large-dimensional covariance matrices
Olivier Ledoit and Michael Wolf · 2012
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Condition-number-regularized covariance estimation
Joong-Ho Won, Johan Lim, Seung-Jean Kim, and Bala Rajaratnam · 2012
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Reconstruction of a low-rank matrix in the presence of Gaussian noise
Andrey a. Shabalin and Andrew B. Nobel · 2013
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Variance estimation and goodness-of-fit test in a high-dimensional strict factor model
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Minimax Risk of Matrix Denoising by Singular Value Thresholding
D. L. Donoho and M. Gavish · 2013
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The Optimal Hard Threshold for Singular Values is 4/ 3 \sqrt{3}
M. Gavish and D. L. Donoho · 2014
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http://dlmf.nist.gov/, Release 1.0.9 of 2014-08-29
NIST Digital Library of Mathematical Functions · 2014
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David L. Donoho, Matan Gavish, and Iain M. Johnstone · 2016
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