Shrinkage Estimators for Covariance Matrices

By Michael J. Daniels, Robert E. Kass. 2001

273 citations recorded by the source corpus.

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In Statistics and Probability

Citations in the corpus

DART: Noise Injection for Robust Imitation Learning (2017, methodology): “Inspired by shrinkage estimation [3], we can obtain a better estimate of ˆ ψ by a target value based on the anticipated ﬁnal robot’s error and subsequently scaling the current simulated error to this level.”
Optimal estimation of a large-dimensional covariance matrix under Stein’s loss (2018, unknown): “For example, see the articles by Haff (1980), Lin and Perlman (1985), Dey and Srinivasan (1985), Daniels and Kaas (2001), Ledoit and Wolf (2004, 2012), Chen et al.”
Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging (2009, methodology): “For example, Cholesky decompositions are frequently used for modeling longitudinal data, both with Bayesian and random eﬀect models [e.g., see Daniels and Kass (2001); Chen and Dunson (2003); Pourahmadi (2007)].”
Statistical Applications in Genetics and Molecular Biology A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics (2011, unknown): “Daniels and Kass (2001) provide a fairly extensive review of empirical Bayes shrinkage estimators proposed in recent years.”
Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices (2008, background): “Bayesian (e.g., Brown, Fearn, and Haque 1999; Daniels and Kass 2001) and minimax approaches (Dey and Srinivasan 1985) have been proposed to regularize ̂ by shrinking sample eigenvalues.”
Covariance Estimation: The GLM and Regularization Perspectives (2011, background): “has been redicovered recently by Dégerine and Lambert-Lacroix (2003), Kurowicka and Cooke (2003) and Joe (2006), but its origin can be traced to a notable and somewhat neglected paper of Yule (1907), equation (25). The identity (25) plays a central role in Joe’s (2006) method of generating random co”
Theoretical Analysis of Bayesian Matrix Factorization (2011, background): “For matrix estimation (L > 1), a variety of estimators which shrink singular values have been proposed (Stein, 1975; Ledoit and Wolf, 2004; Daniels and Kass, 2001), and were shown to possess nice properties under different criteria.”
Near-optimal sensor placements in Gaussian processes (2005, unknown): “Shrinking the eigenvalues of S (Stein, 1975; Ledoit and Wolf, 2004) or shrinking the estimator towards a simpler full-rank matrix (Daniels and Kass, 2001) addresses these problems.”
Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies (2008, unknown): “Shrinking the eigenvalues of S (Stein, 1975; Ledoit and Wolf, 2004) or shrinking the estimator towards a simpler full-rank matrix (Daniels and Kass, 2001) addresses these problems.”
High Dimensional Statistical Inference and Random Matrices (2006, background): “le of the replusion of eigenvalues induced by the Vandermonde term in (4). It also complicates the estimation of population covariancematrices – also a long standing problem, discussed for example in [27, 47, 66, 85, 98]. The Quarter Circle Law Marˇcenko and Pastur [69] gave a systematic description”
High‐dimensional covariance matrix estimation (2019, background): “For instance, Daniels and Kass (2001) proposed several Bayesian estimators which shrink the eigenvalues of the sample covariance matrix, possibly towards a structure.”
Quadratic Shrinkage for Large Covariance Matrices (2020, background): “Stein’s estimator broke new ground and fathered an extensive literature on rotation-equivariant shrinkage estimation of a covariance matrix; for example, see the articles by Chen, Wiesel and Hero (2009), Daniels and Kass (2001), Dey and Srinivasan (1985), Donoho, Gavish and Johnstone (2018), Efron a”