Paper Info
Title
Optimal high-dimensional shrinkage covariance estimation for elliptical distributions.
Abstract
We derive an optimal shrinkage sample covariance matrix (SCM) estimator which is suitable for high dimensional problems and when sampling from an unspecified elliptically symmetric distribution. Specifically, we derive the optimal (oracle) shrinkage parameters that obtain the minimum mean-squared error (MMSE) between the shrinkage SCM and the true covariance matrix when sampling from an elliptical distribution. Subsequently, we show how the oracle shrinkage parameters can be consistently estimated under the random matrix theory regime. Simulations show the advantage of the proposed estimator over the conventional shrinkage SCM estimator due to Ledoit and Wolf (2004). The proposed shrinkage SCM estimator often provides significantly better performance than the Ledoit-Wolf estimator and has the advantage that consistency is guaranteed over the whole class of elliptical distributions with finite 4th order moments.
Year
DOI
Venue
2017
10.23919/EUSIPCO.2017.8081487
European Signal Processing Conference
Field
DocType
ISSN
Econometrics,Elliptical distribution,Estimation of covariance matrices,Shrinkage estimator,Shrinkage,Symmetric probability distribution,Covariance matrix,Statistics,Mathematics,Estimator,Random matrix
Conference
2076-1465
Citations 
PageRank 
References 
0
0.34
3
Authors
1
Name
Order
Citations
PageRank
Esa Ollila135133.51