Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1145768 | Journal of Multivariate Analysis | 2014 | 14 Pages |
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→∞p→∞ and the sample size n→∞n→∞ so that p/n→c∈(0,+∞)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.
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis
Authors
Taras Bodnar, Arjun K. Gupta, Nestor Parolya,