Independent component models for replicated point processes

TL;DR

This paper introduces a semiparametric independent-component model for analyzing replicated point processes, demonstrating estimator consistency and applying it to spatial crime data in Chicago.

Contribution

It presents a novel semiparametric model for point process intensities with proven estimator properties and practical application to spatial crime analysis.

Findings

Estimators are consistent and asymptotically normal.

Simulation studies show good finite-sample performance.

Applied to Chicago street robberies, revealing spatial distribution patterns.

Abstract

We propose a semiparametric independent-component model for the intensity functions of a point process. When independent replications of the process are available, we show that the estimators are consistent and asymptotically normal. We study the finite-sample behavior of the estimators by simulation, and as an example of application we analyze the spatial distribution of street robberies in the city of Chicago.