Gamma Kernel Intensity Estimation in Temporal Point Processes

Abstract

In this article, we propose a nonparametric approach for estimating the intensity function of temporal point processes based on kernel estimators. In particular, we use asymmetric kernel estimators characterized by the gamma distribution, in order to describe features of observed point patterns adequately. Some characteristics of these estimators are analyzed and discussed both through simulated results and applications to real data from different seismic catalogs.

Keywords:

• Bounded domain
• Gamma kernel estimator
• Intensity function
• Temporal point processes

Mathematics Subject Classification:

• 60G55
• 62G07

Acknowledgment

The authors thank the reviewers for their useful comments and suggestions which improved the quality of the article.