DeepAI AI Chat
Log In Sign Up

Optimal shrinkage covariance matrix estimation under random sampling from elliptical distributions

08/30/2018
by   Esa Ollila, et al.
0

This paper considers the problem of estimating a high-dimensional (HD) covariance matrix when the sample size is smaller, or not much larger, than the dimensionality of the data, which could potentially be very large. We develop a regularized sample covariance matrix (RSCM) estimator which can be applied in commonly occurring sparse data problems. The proposed RSCM estimator is based on estimators of the unknown optimal (oracle) shrinkage parameters that yield the minimum mean squared error (MMSE) between the RSCM and the true covariance matrix when the data is sampled from an unspecified elliptically symmetric distribution. We propose two variants of the RSCM estimator which differ in the approach in which they estimate the underlying sphericity parameter involved in the theoretical optimal shrinkage parameter. The performance of the proposed RSCM estimators are evaluated with numerical simulation studies. In particular when the sample sizes are low, the proposed RSCM estimators often show a significant improvement over the conventional RSCM estimator by Ledoit and Wolf (2004). We further evaluate the performance of the proposed estimators in classification and portfolio optimization problems with real data wherein the proposed methods are able to outperform the benchmark methods.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/17/2020

Shrinking the eigenvalues of M-estimators of covariance matrix

A highly popular regularized (shrinkage) covariance matrix estimator is ...
09/03/2021

Regularized tapered sample covariance matrix

Covariance matrix tapers have a long history in signal processing and re...
10/19/2018

Linear Shrinkage Estimation of Covariance Matrices Using Low-Complexity Cross-Validation

Shrinkage can effectively improve the condition number and accuracy of c...
11/09/2020

Coupled regularized sample covariance matrix estimator for multiple classes

The estimation of covariance matrices of multiple classes with limited t...
04/14/2023

Ledoit-Wolf linear shrinkage with unknown mean

This work addresses large dimensional covariance matrix estimation with ...
12/05/2014

Multi-Target Shrinkage

Stein showed that the multivariate sample mean is outperformed by "shrin...
12/14/2021

The Oracle estimator is suboptimal for global minimum variance portfolio optimisation

A common misconception is that the Oracle eigenvalue estimator of the co...