A New Class of Estimators for the N-point Correlations

TL;DR

This paper introduces a new class of estimators for N-point correlation functions that significantly improve variance convergence in galaxy clustering analysis, offering a unified framework with efficient edge correction capabilities.

Contribution

The paper presents a novel class of estimators that outperform existing methods in variance convergence and unify various statistical tools for spatial correlation analysis.

Findings

Variance converges faster to the continuum value in weak clustering

Explicit variance formulas for Poisson and multinomial processes

Includes many existing statistical tools with efficient edge corrections

Abstract

A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to the continuum value much faster than with any alternative, all terms giving rise to a slower convergence exactly cancel. Explicit variance formulae are provided for both Poisson and multinomial point processes using techniques for spatial statistics reported by Ripley (1988). The formalism naturally includes most previously used statistical tools such as N-point correlation functions and their Fourier counterparts, moments of counts-in-cells, and moment correlators. For all these, and perhaps some other statistics our estimator provides a straightforward means for efficient edge corrections.