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：我们研究了给定独立同分布路径重复观测值的高维非平稳 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 和 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说明了其性能。