  We study the uncertainty in different two-point correlation function (2PCF)
estimators in currently available galaxy surveys. This is motivated by the
active subject of using the baryon acoustic oscillations (BAOs) feature in the
correlation function as a tool to constrain cosmological parameters, which
requires a fine analysis of the statistical significance. We discuss how
estimators are affected by both the uncertainty in the mean density $\bar{n}$
and the integral constraint $\frac{1}{V^2}\int_{V^2} \hat{\xi} (r) d^3r =0$
which necessarily causes a bias. We quantify both effects for currently
available galaxy samples using simulated mock catalogues of the Sloan Digital
Sky Survey (SDSS) following a lognormal model, with a Lambda-Cold Dark Matter
($\Lambda\text{CDM}$) correlation function and similar properties as the
samples (number density, mean redshift for the $\Lambda\text{CDM}$ correlation
function, survey geometry, mass-luminosity bias). Because we need extensive
simulations to quantify small statistical effects, we cannot use realistic
N-body simulations and some physical effects are neglected. Our simulations
still enable a comparison of the different estimators by looking at their
biases and variances. We also test the reliability of the BAO detection in the
SDSS samples and study the compatibility of the data results with our
$\Lambda\text{CDM}$ simulations.
