Estimation of spatial-temporal point process models using a Stoyan-Grabarnik statistic

Frederic P. Schoenberg

Submitted June 2, 2022, SCEC Contribution #11814

Parameters in spatial-temporal point process models are typically fit by maximum likelihood estimation (MLE), or some close variant. Here, we show that such parameters can instead be estimated consistently, under general conditions, by instead minimizing the Stoyan-Grabarnik (SG) statistic. More specifically, the spatial-temporal region is divided up into cells, and the sum of squares of the SG statistic is minimized. The resulting estimator has desirable properties, is extremely easy and quick to compute, and does not require approximation of the pesky integral in the logl-likelihood formula. Examples and applications to crimes and earthquakes are presented.

Citation
Schoenberg, F. P. (2022, 06). Estimation of spatial-temporal point process models using a Stoyan-Grabarnik statistic. Oral Presentation at METMA.