Median-based estimation of the intensity of a spatial point process

TL;DR

This paper introduces a median-based estimator for the intensity of stationary spatial point processes, demonstrating its robustness and asymptotic properties through theoretical analysis and simulations.

Contribution

The paper proposes a novel median-based estimator for spatial point process intensity, providing theoretical guarantees and empirical evidence of its robustness over traditional methods.

Findings

The median-based estimator is consistent and asymptotically normal.

It is more robust to outliers than the standard mean-based estimator.

Simulation results confirm the theoretical properties and robustness advantages.

Abstract

This paper is concerned with a robust estimator of the intensity of a stationary spatial point process. The estimator corresponds to the median of a jittered sample of the number of points, computed from a tessellation of the observation domain. We show that this median-based estimator satisfies a Bahadur representation from which we deduce its consistency and asymptotic normality under mild assumptions on the spatial point process. Through a simulation study, we compare the new estimator with the standard one counting the mean number of points per unit volume. The empirical study verifies the asymptotic properties established and shows that the median-based estimator is more robust to outliers than the standard estimator.