On Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model

TL;DR

This paper provides new theoretical insights and improved error bounds for Dantzig and Lasso estimators of the drift in high-dimensional Ornstein-Uhlenbeck models, including oracle inequalities and finite sample analysis.

Contribution

It introduces improved rates and proves the restricted eigenvalue property under ergodicity, advancing the understanding of these estimators in high-dimensional stochastic processes.

Findings

Enhanced error bounds for estimators

Proved restricted eigenvalue property under ergodicity

Numerical analysis of finite sample performance

Abstract

In this paper we present new theoretical results for the Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model under sparsity constraints. Our focus is on oracle inequalities for both estimators and error bounds with respect to several norms. In the context of the Lasso estimator our paper is strongly related to [11], who investigated the same problem under row sparsity. We improve their rates and also prove the restricted eigenvalue property solely under ergodicity assumption on the model. Finally, we demonstrate a numerical analysis to uncover the finite sample performance of the Dantzig and Lasso estimators.