Unbiased risk estimation method for covariance estimation

TL;DR

This paper introduces an unbiased risk estimation method for covariance estimation, enabling effective model selection with theoretical guarantees and demonstrated through simulations.

Contribution

It develops a new unbiased risk estimation approach for covariance matrices, providing oracle inequalities and practical validation.

Findings

The method accurately estimates covariance risk.

The selected estimator performs close to the oracle.

Simulations confirm the approach's efficiency.

Abstract

We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (URE) method, we build an estimator of the risk which allows to select an estimator in a collection of model. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.