On Lasso and Slope drift estimators for Lévy-driven Ornstein-Uhlenbeck processes

Niklas Dexheimer; Claudia Strauch

doi:10.3150/22-BEJ1574

On Lasso and Slope drift estimators for Lévy-driven Ornstein-Uhlenbeck processes

^*Corresponding author for this work

Department of Mathematics

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2 Citations (Scopus)

Abstract

We investigate the problem of estimating the drift parameter of a high-dimensional Lévy-driven Ornstein– Uhlenbeck process under sparsity constraints. It is shown that both Lasso and Slope estimators achieve the min-imax optimal rate of convergence (up to numerical constants), for tuning parameters chosen independently of the confidence level, which improves the previously obtained results for standard Ornstein–Uhlenbeck processes.

Original language	English
Journal	Bernoulli
Volume	30
Issue	1
Pages (from-to)	88-116
Number of pages	29
ISSN	1350-7265
DOIs	https://doi.org/10.3150/22-BEJ1574
Publication status	Published - Feb 2024

Keywords

High-dimensional statistics
Lasso
Ornstein–Uhlenbeck process
Slope
parametric statistics
sparse estimation

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10.3150/22-BEJ1574

https://arxiv.org/abs/2205.07813

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KW - High-dimensional statistics

KW - Lasso

KW - Ornstein–Uhlenbeck process

KW - Slope

KW - parametric statistics

KW - sparse estimation

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On Lasso and Slope drift estimators for Lévy-driven Ornstein-Uhlenbeck processes

Abstract

Keywords

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