Adaptive Covariance Estimation with model selection

TL;DR

This paper introduces an adaptive penalized method for selecting covariance models from i.i.d. data, extending previous work with a data-driven penalty that guarantees an oracle inequality.

Contribution

It generalizes existing covariance estimation techniques by incorporating a fully adaptive, data-driven penalty in a matricial regression framework.

Findings

Provides a new adaptive covariance estimation procedure

Establishes an oracle inequality for the estimator

Extends previous results to a more general model

Abstract

We provide in this paper a fully adaptive penalized procedure to select a covariance among a collection of models observing i.i.d replications of the process at fixed observation points. For this we generalize previous results of Bigot and al. and propose to use a data driven penalty to obtain an oracle inequality for the estimator. We prove that this method is an extension to the matricial regression model of the work by Baraud.