On the Strong Convergence of the Optimal Linear Shrinkage Estimator for Large Dimensional Covariance Matrix

Taras Bodnar, Arjun K. Gupta and Nestor Parolya

Papers from arXiv.org

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 $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that $p/n\rightarrow c\in (0, +\infty)$. Additionally, we prove that the Frobenius norm of the sample covariance matrix tends almost surely to a deterministic quantity which can be consistently estimated.

Date: 2013-08, Revised 2014-06
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

Published in Journal of Multivariate Analysis, Volume 132, 2014, pp. 215-228

Downloads: (external link)
http://arxiv.org/pdf/1308.2608 Latest version (application/pdf)

Related works:
Journal Article: On the strong convergence of the optimal linear shrinkage estimator for large dimensional covariance matrix (2014)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1308.2608

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().