Measuring galaxy abundance and clustering at high redshift from
  incomplete spectroscopic data: Tests on mock catalogs and application to
  zCOSMOS
  The number density and correlation function of galaxies are two key
quantities to characterize the distribution of the observed galaxy population.
High-$z$ spectroscopic surveys, which usually involve complex target selection
and are incomplete in redshift sampling, present both opportunities and
challenges to measure these quantities reliably in the high-$z$ Universe. Using
realistic mock catalogs we show that target selection and redshift
incompleteness can lead to significantly biased results. We develop methods to
correct such bias, using information provided by the parent photometric data
from which the spectroscopic sample is constructed. Our tests using realistic
mock samples show that our methods are able to reproduce the true stellar mass
function and correlation function reliably. As applications, mock catalogs are
constructed for two high-z surveys: the existing zCOSMOS-bright galaxy sample
and the forthcoming PFS galaxy evolution survey. We apply our methods to the
zCOSMOS-bright sample and make comparisons with results obtained before. The
same set of mock samples are used to quantify cosmic variances expected for
different sample sizes. We find that, for both number density and correlation
function, the relative error due to cosmic variance in the PFS galaxy survey
will be reduced by a factor of 3-4 when compared to zCOSMOS.
