论文标题
霍克斯流程和Edgeworth扩展，并应用于最大似然估计器
Hawkes process and Edgeworth expansion with application to maximum likelihood estimator
论文作者
论文摘要
Hawks过程是具有自我激发属性的点过程。它已用于建模地震，社交媒体事件，感染等，并引起了很多关注。但是，作为一个真正的问题，在某些情况下，我们无法以足够的观察时间获得数据。在这种情况下，不适合通过正态分布估算估计器的误差分布。为了克服这个问题，我们为具有指数核的一维鹰队过程的高阶渐近行为提供了严格的数学基础。作为一个重要的应用，我们为指数霍克斯过程的最大似然估计器提供了二阶渐近分布。此外，我们还提供了仿真结果。
The Hawks process is a point process with a self-exciting property. It has been used to model earthquakes, social media events, infections, etc., and is getting a lot of attention. However, as a real problem, there are often situations where we can not obtain data with sufficient observation time. In such cases, it is not appropriate to approximate the error distribution of an estimator by the normal distribution. To overcome this problem, we provide a rigorous mathematical foundation of the theory for the higher-order asymptotic behavior of the one-dimensional Hawkes process with an exponential kernel. As an important application, we give the second-order asymptotic distribution for the maximum likelihood estimator of the exponential Hawkes process. Furthermore, we also present the simulation results.
