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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:132

Article

Bodnar, Taras¹  Gupta, Arjun K.²  Parolya, Nestor³ 

[1] Humboldt Univ, Dept Math, D-10099 Berlin, Germany

[2] Bowling Green State Univ, Dept Math & Stat, Bowling Green, OH 43403 USA

[3] Leibniz Univ Hannover, Inst Empir Finance Econometr, D-30167 Hannover, Germany

关键词: Large-dimensional asymptotics;    Random matrix theory;    Covariance matrix estimation;   

DOI  :  10.1016/j.jmva.2014.08.006

来源: Elsevier

【 摘 要 】

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 -> infinity and the sample size n -> infinity so that p/n -> c is an element of (0, +infinity). Additionally, we prove that the Frobenius norm of the sample covariance matrix tends almost surely to a deterministic quantity which can be consistently estimated. Published by Elsevier Inc.

【 授权许可】

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