High-Dimensional Covariance Matrix Estimation: Shrinkage Toward a Diagonal Target

Sakai Ando and Mingmei Xiao

No 2023/257, IMF Working Papers from International Monetary Fund

Abstract: This paper proposes a novel shrinkage estimator for high-dimensional covariance matrices by extending the Oracle Approximating Shrinkage (OAS) of Chen et al. (2009) to target the diagonal elements of the sample covariance matrix. We derive the closed-form solution of the shrinkage parameter and show by simulation that, when the diagonal elements of the true covariance matrix exhibit substantial variation, our method reduces the Mean Squared Error, compared with the OAS that targets an average variance. The improvement is larger when the true covariance matrix is sparser. Our method also reduces the Mean Squared Error for the inverse of the covariance matrix.

Keywords: High-Dimension; Covariance Matrix; Shrinkage; Diagonal Target; matrix estimation; shrinkage parameter; novel shrinkage estimator; sample correlation matrix; Estimation techniques (search for similar items in EconPapers)
Pages: 32
Date: 2023-12-08
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