Diagnostics for nonparametric estimation in space-time seismic processes

In this paper we propose a nonparametric method, based on locally variable bandwidthskernel estimators, to describe the space-time variation of seismic activity of aregion of Southern California. The flexible estimation approach is introduced togetherwith a diagnostic method for space-time point process, based on the interpretation ofsome second-order statistics, to analyze the dependence structure of observed data andsuggest directions for fit improvement. In this paper we review a diagnostic method forspace-time point processes based on the interpretation of the transformed version of somesecond-order statistics. The method is useful to analyze dependence structures of observeddata and suggests directions for fit improvement also when a more flexible estimator of theconditional intensity function is used, such as the kernel one. In particular locally variablebandwidths kernel estimators are used to describe space-time variations of seismic activityof a region of Southern California.