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The number density and correlation function of galaxies are two keyquantities to characterize the distribution of the observed galaxy population.High-$z$ spectroscopic surveys, which usually involve complex target selectionand are incomplete in redshift sampling, present both opportunities andchallenges to measure these quantities reliably in the high-$z$ Universe. Usingrealistic mock catalogs we show that target selection and redshiftincompleteness can lead to significantly biased results, especially due to theflux limit selection criteria. We develop a new method to correct the fluxlimit effect, using information provided by the parent photometric data fromwhich the spectroscopic sample is constructed. Our tests using realistic mocksamples show that the method is able to reproduce the true stellar massfunction and correlation function reliably. Mock catalogs are constructed forthe existing zCOSMOS and VIPERS surveys, as well as for the forthcoming PFSgalaxy evolution survey. The same set of mock samples are used to quantify thetotal variance expected for different sample sizes. We find that the totalvariance decreases very slowly when the survey area reaches about 4 deg$^2$ forthe abundance and about 8 deg$^2$ for the clustering, indicating that thecosmic variance is no longer the dominant source of error for PFS-like surveys.We also quantify improvements expected in the PFS-like galaxy survey relativeto zCOSMOS and VIPERS surveys.

Measuring galaxy abundance and clustering at high redshift from incomplete spectroscopic data: Tests on mock catalogs