Standard and robust intensity parameter estimation for stationary determinantal point processes

TL;DR

This paper compares standard and median-based estimators for the intensity parameter of stationary determinantal point processes, demonstrating their consistency, asymptotic normality, and efficiency through simulations.

Contribution

It introduces a median-based estimator for the intensity of determinantal point processes and analyzes its theoretical properties and practical performance.

Findings

Both estimators are consistent and asymptotically normal.

The median-based estimator shows robustness to outliers.

Simulation results confirm the efficiency of the proposed methods.

Abstract

This work is concerned with the estimation of the intensity parameter of a stationary determinantal point process. We consider the standard estimator, corresponding to the number of observed points per unit volume and a recently introduced median-based estimator more robust to outliers. The consistency and asymptotic normality of estimators are obtained under mild assumptions on the determinantal point process. We illustrate the efficiency of the procedures in a simulation study.