论文标题
可变生产力的非参数估计霍克斯工艺
Nonparametric estimation of variable productivity Hawkes processes
论文作者
论文摘要
考虑生产率可变的霍克斯模型的扩展。特别是，考虑到每个点可能具有其自身生产率的情况，并且为这些生产力的最大似然估计量提供了简单的分析公式。将该估计量与经验估计量进行比较，并通过降低截断，平滑和重新估算估计值来探索稳定两个估计器的方法。在模拟中探索了估计器的性能，并将方法应用于地震学和流行数据集以显示和量化生产率的实质性差异。
An extension of the Hawkes model where the productivity is variable is considered. In particular, the case is considered where each point may have its own productivity and a simple analytic formula is derived for the maximum likelihood estimators of these productivities. This estimator is compared with an empirical estimator and ways are explored of stabilizing both estimators by lower truncating, smoothing, and rescaling the estimates. Properties of the estimators are explored in simulations, and the methods are applied to seismological and epidemic datasets to show and quantify substantial variation in productivity.
