A shrinkage estimation for large dimensional precision matrices using random matrix theory

TL;DR

This paper introduces a new distribution-free ridge-type shrinkage estimator for large-dimensional precision matrices, leveraging random matrix theory to derive asymptotic optimal coefficients and demonstrate improved performance.

Contribution

It proposes a novel explicit formula for a shrinkage estimator that is applicable in high-dimensional settings without structural assumptions, based on random matrix theory.

Findings

The estimator performs well across various high-dimensional scenarios.

It outperforms existing methods in numerical simulations.

The approach is distribution-free and does not require covariance structure assumptions.

Abstract

In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were also conducted based on the asymptotic results deriving from random matrix theories. The new estimator which has a simple explicit formula is distribution-free and applicable to situation where the dimension of observation is greater than the sample size. Further, no assumptions are required on the structure of the population covariance matrix or the precision matrix. Finally, numerical studies are conducted to examine the performances of the new estimator and existing methods for a wide range of settings.