Reconstructing the shape of the correlation function

TL;DR

This paper introduces a versatile estimator for the correlation function that accurately captures its shape in ensemble averages, even with large-scale correlations, applicable across multiple dimensions and signal types.

Contribution

It presents a novel, general estimator for the correlation function that works for both diffuse and discrete signals and handles large-scale correlations effectively.

Findings

Estimator accurately reconstructs correlation function shape in simulations

Works for signals with significant correlations on survey scales

Applicable to various cosmological and astrophysical data analyses

Abstract

We develop an estimator for the correlation function which, in the ensemble average, returns the shape of the correlation function, even for signals that have significant correlations on the scale of the survey region. Our estimator is general and works in any number of dimensions. We develop versions of the estimator for both diffuse and discrete signals. As an application, we examine Monte Carlo simulations of X-ray background measurements. These include a realistic, spatially-inhomogeneous population of spurious detector events. We discuss applying the estimator to the averaging of correlation functions evaluated on several small fields, and to other cosmological applications.