Adaptive estimating function inference for non-stationary determinantal point processes

TL;DR

This paper develops a general asymptotic normality theory for estimating functions in non-stationary point processes, introduces an adaptive, data-driven truncation method for determinantal point processes, and demonstrates its effectiveness through simulations and real data.

Contribution

It provides the first asymptotic normality results for estimating functions in non-stationary point processes and proposes an adaptive truncation method for determinantal point processes.

Findings

The adaptive truncation method improves estimation accuracy.

Simulation studies show the method's robustness.

Application to real data confirms practical utility.

Abstract

Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this paper we establish asymptotic normality of estimating function estimators in a very general setting of non-stationary point processes. We then adapt this result to the case of non-stationary determinantal point processes which are an important class of models for repulsive point patterns. In practice often first and second order estimating functions are used. For the latter it is common practice to omit contributions for pairs of points separated by a distance larger than some truncation distance which is usually specified in an ad hoc manner. We suggest instead a data-driven approach where the truncation distance is adapted automatically to the point process being fitted and where the approach integrates seamlessly with our asymptotic framework. The good performance of the adaptive approach is illustrated via simulation studies for non-stationary determinantal point processes and by an application to a real dataset.