Unbiased Estimators for Correlation Measurements

TL;DR

This paper derives correction formulas for unbiased correlation estimators in small samples, improving accuracy and efficiency in statistical measurements across various fields.

Contribution

It introduces new correction formulas for bias reduction in correlation measurements, especially effective for small event samples.

Findings

Correction formulas effectively reduce bias in small samples.

Application to a simple correlation model demonstrates utility.

Highlights importance for single-event measurements in astrophysics and collider experiments.

Abstract

Higher order correlation measurements involve multiple event averages which must run over unequal events to avoid statistical bias. We derive correction formulas for small event samples, where the bias is largest, and utilize the results to achieve savings in CPU time consumption for the star integral. Results from a simple model of correlations illustrate the utility and importance of these corrections. Single-event correlation measurements such as in galaxy distributions and envisaged at RHIC must take great care to avoid this unnecessary pitfall.