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

Shogo Nakakita

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arXiv · 2510.21505

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

Shogo Nakakita

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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.

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Shogo Nakakita. 2025-10-24. Sparse estimation for the drift of high-dimensional Ornstein--Uhlenbeck processes with i.i.d. paths. https://arxiv.org/abs/2510.21505

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