Angular Correlation Function Estimators Accounting for Contamination
  from Probabilistic Distance Measurements
  With the advent of surveys containing millions to billions of galaxies, it is
imperative to develop analysis techniques that utilize the available
statistical power. In galaxy clustering, even small sample contamination
arising from distance uncertainties can lead to large artifacts, which the
standard estimator does not account for. We first introduce a formalism, termed
decontamination, that corrects for sample contamination by utilizing the
observed cross-correlations in the contaminated samples; this corrects any
correlation function estimator for contamination. Using this formalism, we
present a new estimator that uses the standard estimator to measure correlation
functions in the contaminated samples but then corrects for contamination. We
also introduce a weighted estimator that assigns each galaxy a weight in each
redshift bin based on its probability of being in that bin. We demonstrate that
these estimators effectively recover the true correlation functions and their
covariance matrices. Our estimators can correct for sample contamination caused
by misclassification between object types as well as photometric redshifts;
they should be particularly helpful for studies of galaxy evolution and
baryonic acoustic oscillations, where forward-modeling the clustering signal
using the contaminated redshift distribution is undesirable.
