# Orthogonal series estimation of the pair correlation function of a spatial point process

## TL;DR

This paper introduces a new orthogonal series estimator for the pair correlation function in spatial point processes, which is consistent, asymptotically normal, and can outperform kernel estimators especially in clustered patterns.

## Contribution

The paper proposes a novel orthogonal series estimator for the pair correlation function, addressing bias issues in kernel methods for clustered point patterns.

## Key findings

- Estimator is consistent and asymptotically normal.
- Outperforms kernel estimators for Poisson and clustered processes.
- Simulation results support theoretical properties.

## Abstract

The pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. Non-parametric estimation of the pair correlation function is a typical initial step of a statistical analysis of a spatial point pattern. Kernel estimators are popular but especially for clustered point patterns suffer from bias for small spatial lags. In this paper we introduce a new orthogonal series estimator. The new estimator is consistent and asymptotically normal according to our theoretical and simulation results. Our simulations further show that the new estimator can outperform the kernel estimators in particular for Poisson and clustered point processes.