Shrinking the eigenvalues of M-estimators of covariance matrix

06/17/2020
by   Esa Ollila, et al.
0

A highly popular regularized (shrinkage) covariance matrix estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward the grand mean of the eigenvalues of the SCM. In this paper, a more general approach is considered in which the SCM is replaced by an M-estimator of scatter matrix and a fully automatic data adaptive method to compute the optimal shrinkage parameter with minimum mean squared error is proposed. Our approach permits the use of any weight function such as Gaussian, Huber's, Tyler's, or t-weight functions, all of which are commonly used in M-estimation framework. Our simulation examples illustrate that shrinkage M-estimators based on the proposed optimal tuning combined with robust weight function do not loose in performance to shrinkage SCM estimator when the data is Gaussian, but provide significantly improved performance when the data is sampled from an unspecified heavy-tailed elliptically symmetric distribution. Also, real-world and synthetic stock market data validate the performance of the proposed method in practical applications.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/12/2020

M-estimators of scatter with eigenvalue shrinkage

A popular regularized (shrinkage) covariance estimator is the shrinkage ...
research
08/30/2018

Optimal shrinkage covariance matrix estimation under random sampling from elliptical distributions

This paper considers the problem of estimating a high-dimensional (HD) c...
research
05/07/2023

Affine equivariant Tyler's M-estimator applied to tail parameter learning of elliptical distributions

We propose estimating the scale parameter (mean of the eigenvalues) of t...
research
10/26/2022

R-NL: Fast and Robust Covariance Estimation for Elliptical Distributions in High Dimensions

We combine Tyler's robust estimator of the dispersion matrix with nonlin...
research
05/18/2018

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

We introduce a distributionally robust maximum likelihood estimation mod...
research
04/14/2023

Ledoit-Wolf linear shrinkage with unknown mean

This work addresses large dimensional covariance matrix estimation with ...

Please sign up or login with your details

Forgot password? Click here to reset