Sample size effects in multivariate fitting of correlated data

TL;DR

This paper investigates how finite sample sizes impact the accuracy of parameter estimates and error bars when fitting models to correlated data, providing corrections for common estimation methods.

Contribution

It introduces approximate corrections for variance estimates of fitted parameters in correlated data analysis, addressing finite sample size effects.

Findings

Finite sample sizes bias variance estimates.

Derived correction formulas for standard error estimates.

Validated corrections through numerical simulations.

Abstract

A common problem in analysis of experiments or in lattice QCD simulations is fitting a parameterized model to the average over a number of samples of correlated data values. If the number of samples is not infinite, estimates of the variance of the parameters ("error bars") and of the goodness of fit are affected. We illustrate these problems with numerical simulations, and calculate approximate corrections to the variance of the parameters for estimates made in the standard way from derivatives of the parameters' probability distribution as well as from jackknife and bootstrap estimates.