论文标题
在莱维驱动的Ornstein的Lasso和斜坡漂移估计器上 - Uhlenbeck过程
On Lasso and Slope drift estimators for Lévy-driven Ornstein--Uhlenbeck processes
论文作者
论文摘要
我们研究了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，对于独立于置信度而选择的调整参数，LASSO和斜率估计器都达到了最小的收敛速率（高达数值常数），从而改善了先前获得的标准Ornstein-Ornstein-uhlenbeck过程的结果。结果是非肿瘤的，并且相对于类似于受限制的特征值条件的事件而言，概率和条件期望。
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 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.
