标题： 关于Lévy驱动的Ornstein-Uhlenbeck过程的Lasso和Slope漂移估计量 显示英文标题

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

摘要： 我们研究在稀疏性约束下估计高维Lévy驱动的Ornstein--Uhlenbeck过程的漂移参数的问题。 结果表明，当调整参数独立于置信水平选择时，Lasso和Slope估计量都能达到最小最大最优收敛率（数值常数除外），这改进了对标准Ornstein--Uhlenbeck过程之前得到的结果。 结果是非渐近的，并且在概率和条件期望下都成立，相对于一个类似于限制特征值条件的事件。 显示英文摘要

摘要： We investigate the problem of estimating the drift parameter of a high-dimensional L\'evy-driven Ornstein--Uhlenbeck process under sparsity constraints. It is shown that both Lasso and Slope estimators achieve the minimax 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. The results are nonasymptotic and hold both in probability and conditional expectation with respect to an event resembling the restricted eigenvalue condition.