Sparse estimation for the drift of high-dimensional Ornstein--Uhlenbeck processes with i.i.d. paths

TL;DR

This paper investigates sparsity-regularized maximum likelihood methods, including Lasso and Slope, for estimating the drift in high-dimensional Ornstein-Uhlenbeck processes, demonstrating their optimal convergence rates and practical performance.

Contribution

It introduces the use of Lasso and Slope estimators for high-dimensional Ornstein-Uhlenbeck processes and proves their minimax optimal convergence rates.

Findings

Lasso and Slope estimators achieve minimax optimal convergence rates.

Numerical experiments confirm the effectiveness of sparse estimation methods.

The methods are applicable to high-dimensional non-stationary Ornstein-Uhlenbeck processes.

Abstract

We study sparsity-regularized maximum likelihood estimation for the drift parameter of high-dimensional non-stationary Ornstein--Uhlenbeck processes given repeated measurements of i.i.d. paths. In particular, we show that Lasso and Slope estimators can achieve the minimax optimal rate of convergence. We exhibit numerical experiments for sparse estimation methods and show their performance.