On the strong convergence of the optimal linear shrinkage estimator for large dimensional covariance matrix

Taras Bodnar, Arjun K. Gupta and Nestor Parolya

Journal of Multivariate Analysis, 2014, vol. 132, issue C, 215-228

Abstract: In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The developed distribution-free estimators obey almost surely the smallest Frobenius loss over all linear shrinkage estimators for the covariance matrix. The case we consider includes the number of variables p→∞ and the sample size n→∞ so that p/n→c∈(0,+∞). Additionally, we prove that the Frobenius norm of the sample covariance matrix tends almost surely to a deterministic quantity which can be consistently estimated.

Keywords: Large-dimensional asymptotics; Random matrix theory; Covariance matrix estimation (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (15)

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Related works:
Working Paper: On the Strong Convergence of the Optimal Linear Shrinkage Estimator for Large Dimensional Covariance Matrix (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:132:y:2014:i:c:p:215-228

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DOI: 10.1016/j.jmva.2014.08.006

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