Moment analysis of the Delaunay tessellation field estimator

TL;DR

This paper derives explicit formulas for the mean and variance of the Delaunay tessellation field estimator using the Campbell--Mecke theorem, with a focus on Poisson processes, enhancing understanding of its statistical properties.

Contribution

It provides the first explicit expressions for the mean and variance of the Delaunay tessellation field estimator, especially for Poisson processes.

Findings

Explicit mean and variance formulas derived

Focus on Poisson process properties

Improved statistical understanding of the estimator

Abstract

The Campbell--Mecke theorem is used to derive explicit expressions for the mean and variance of Schaap and Van de Weygaert's Delaunay tessellation field estimator. Special attention is paid to Poisson processes.