A Maximum Likelihood Approach to Estimating Correlation Functions
  We define a Maximum Likelihood (ML for short) estimator for the correlation
function, {\xi}, that uses the same pair counting observables (D, R, DD, DR,
RR) as the standard Landy and Szalay (1993, LS for short) estimator. The ML
estimator outperforms the LS estimator in that it results in smaller
measurement errors at any fixed random point density. Put another way, the ML
estimator can reach the same precision as the LS estimator with a significantly
smaller random point catalog. Moreover, these gains are achieved without
significantly increasing the computational requirements for estimating {\xi}.
We quantify the relative improvement of the ML estimator over the LS estimator,
and discuss the regimes under which these improvements are most significant. We
present a short guide on how to implement the ML estimator, and emphasize that
the code alterations required to switch from a LS to a ML estimator are
minimal.
