论文标题
霍克斯流程的光谱估计来自计数数据
Spectral estimation of Hawkes processes from count data
论文作者
论文摘要
本文提出了一种参数估计方法，用于未观察到的线性固定鹰工艺。当未观察到点的确切位置，而仅观察到固定尺寸的时间间隔的计数时，基于可能性的方法是不可行的。我们表明，基于Whittle方法的光谱估计适用于此情况，并提供一致且渐近的正常估计器，为生殖功能提供了轻度的力矩条件。模拟数据集和一个案例研究说明了估计的性能，即使时间间隔相对较大，尤其是繁殖函数的性能。
This paper presents a parametric estimation method for ill-observed linear stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, methods based on the likelihood are not feasible. We show that spectral estimation based on Whittle's method is adapted to this case and provides consistent and asymptotically normal estimators, provided a mild moment condition on the reproduction function. Simulated datasets and a case-study illustrate the performances of the estimation, notably of the reproduction function even when time intervals are relatively large.
