论文标题
Lepskiĭ型停止规则，以进行多维lévy过程的协方差估算
A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes
论文作者
论文摘要
我们假设在离散时间点观察到了莱维过程。从lévyKhinchine特征连续部分的渐近最小估计量开始，即协方差，我们得出了一个数据驱动的参数选择，以估计协方差频率。我们研究了自适应程序的Lepskiĭ型停止规则。因此，我们使用平衡原理作为最佳数据驱动参数。自适应估计器几乎达到了最佳速率。还提出了具有建议的选择规则的数值实验。
We suppose that a Lévy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the Lévy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covariance. We investigate a Lepskiĭ-type stopping rule for the adaptive procedure. Consequently, we use a balancing principle for the best possible data-driven parameter. The adaptive estimator achieves almost the optimal rate. Numerical experiments with the proposed selection rule are also presented.
