An optimized correlation function estimator for galaxy surveys
  Measuring the two-point correlation function of the galaxies in the Universe
gives access to the underlying dark matter distribution, which is related to
cosmological parameters and to the physics of the primordial Universe. The
estimation of the correlation function for current galaxy surveys makes use of
the Landy-Szalay estimator, which is supposed to reach minimal variance. This
is only true, however, for a vanishing correlation function. We study the
Landy-Szalay estimator when these conditions are not fulfilled and propose a
new estimator that provides the smallest variance for a given survey geometry.
Our estimator is a linear combination of ratios between paircounts of data
and/or random catalogues (DD, RR and DR). The optimal combination for a given
geometry is determined by using lognormal mock catalogues. The resulting
estimator is biased in a model-dependent way, but we propose a simple iterative
procedure for obtaining an unbiased model- independent estimator.Our method can
be easily applied to any dataset and requires few extra mock catalogues
compared to the standard Landy-Szalay analysis. Using various sets of simulated
data (lognormal, second-order LPT and N-Body), we obtain a 20-25% gain on the
error bars on the two-point correlation function for the SDSS geometry and
$\Lambda$CDM correlation function. When applied to SDSS data (DR7 and DR9), we
achieve a similar gain on the correlation functions, which translates into a
10-15% improvement over the estimation of the densities of matter $\Omega_m$
and dark energy $\Omega_\Lambda$ in an open $\Lambda$CDM model. The constraints
derived from DR7 data with our estimator are similar to those obtained with the
DR9 data and the Landy-Szalay estimator, which covers a volume twice as large
and has a density that is three times higher.
