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2020 On Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model
Gabriela Ciołek, Dmytro Marushkevych, Mark Podolskij
Electron. J. Statist. 14(2): 4395-4420 (2020). DOI: 10.1214/20-EJS1775

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], where the same problem was investigated 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.

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Gabriela Ciołek. Dmytro Marushkevych. Mark Podolskij. "On Dantzig and Lasso estimators of the drift in a high dimensional Ornstein-Uhlenbeck model." Electron. J. Statist. 14 (2) 4395 - 4420, 2020. https://doi.org/10.1214/20-EJS1775

Information

Received: 1 July 2020; Published: 2020
First available in Project Euclid: 24 December 2020

MathSciNet: MR4194266
Digital Object Identifier: 10.1214/20-EJS1775

Subjects:
Primary: 60G15, 62M05
Secondary: 62H12, 62M99

JOURNAL ARTICLE
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Vol.14 • No. 2 • 2020
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