 Improved Stein-type shrinkage estimators for the high-dimensional multivariate normal covariance matrixThomas J. Fisher and Xiaoqian Sun Computational Statistics & Data Analysis, 2011, vol. 55, issue 5, 1909-1918 Abstract: Many applications require an estimate for the covariance matrix that is non-singular and well-conditioned. As the dimensionality increases, the sample covariance matrix becomes ill-conditioned or even singular. A common approach to estimating the covariance matrix when the dimensionality is large is that of Stein-type shrinkage estimation. A convex combination of the sample covariance matrix and a well-conditioned target matrix is used to estimate the covariance matrix. Recent work in the literature has shown that an optimal combination exists under mean-squared loss, however it must be estimated from the data. In this paper, we introduce a new set of estimators for the optimal convex combination for three commonly used target matrices. A simulation study shows an improvement over those in the literature in cases of extreme high-dimensionality of the data. A data analysis shows the estimators are effective in a discriminant and classification analysis. Keywords: Covariance; matrix; Shrinkage; estimation; High-dimensional; data; analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:55:y:2011:i:5:p:1909-1918 Access Statistics for this article Computational Statistics & Data Analysis is currently edited by S.P. Azen More articles in Computational Statistics & Data Analysis from Elsevier |
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