论文标题
时空过程的强度函数的自适应内核估计器
An adaptive kernel estimator for the intensity function of spatio-temporal point processes
论文作者
论文摘要
在时空点模式分析中，主要统计目标之一是估计一阶强度函数，即每单位面积和单位时间的预期点数。该估计通常是通过内核函数非参数进行的，其中最常见的障碍之一是在估计之前选择核带宽。这项工作提出了一种强度估计机制，其中每个数据点的空间和时间带宽在时空点模式下都会变化。这类估计器称为自适应估计器，尽管在空间环境中进行了研究，但在时空环境中几乎没有说过它们。我们在时空上下文中定义了自适应强度估计器，并根据带宽分位数扩展了分区技术以执行快速估计。我们通过模拟证明，该技术在近似直接估计器和更快的计算时间的分区估计器中效果很好。最后，我们应用我们的方法来估计亚马逊盆地中火灾的时空强度。
In spatio-temporal point pattern analysis, one of the main statistical objectives is to estimate the first-order intensity function, i.e., the expected number of points per unit area and unit time. This estimation is usually carried out non-parametrically through kernel functions, where one of the most frequent handicaps is the selection of kernel bandwidths prior to estimation. This work presents an intensity estimation mechanism in which the spatial and temporal bandwidths change at each data point in a spatio-temporal point pattern. This class of estimators is called adaptive estimators, and although there have been studied in spatial settings, little has been said about them in the spatio-temporal context. We define the adaptive intensity estimator in the spatio-temporal context and extend a partitioning technique based on the bandwidths quantiles to perform a fast estimation. We demonstrate through simulation that this technique works well in practice with the partition estimator approximating the direct estimator and much faster computation time. Finally, we apply our method to estimate the spatio-temporal intensity of fires in the Amazonia basin.
