This paper presents a kriging method for spatial prediction of temporal intensity functions, for situations where a temporal point process is observed at different spatial locations. Assuming that several replications of the process are available at the spatial sites, this method avoids assumptions like isotropy, which are not valid in many applications. As part of the derivations, new nonparametric estimators for the mean and covariance functions of temporal point processes are introduced, and their properties are studied theoretically and by simulation. The method is applied to the analysis of bike demand patterns in the Divvy bicycle sharing system of the city of Chicago.

本文提出了一种用于时间强度函数空间预测的克里金方法，适用于在不同空间位置观察到时间点过程的情况。假设在空间站点上可以多次复制该过程，该方法避免了诸如各向同性之类的假设，这些假设在许多应用中都无效。作为推导的一部分，引入了新的时间点过程均值和协方差函数的非参数估计量，并通过理论和仿真研究了它们的性质。该方法应用于芝加哥市 Divvy 自行车共享系统中的自行车需求模式分析。