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.

翻译：本文研究基于独立同分布路径重复观测的高维非平稳Ornstein--Uhlenbeck过程漂移参数的稀疏正则化极大似然估计。特别地，我们证明了Lasso与Slope估计量能够达到极小极大最优收敛速率。我们展示了稀疏估计方法的数值实验，并验证了其性能表现。