The Incomplete Conditional Stellar Mass Function: Unveiling the Stellar
  Mass Functions of Galaxies at 0.1 < Z < 0.8 from BOSS Observations
  We propose a novel method to constrain the missing fraction of galaxies using
galaxy clustering measurements in the galaxy conditional stellar mass function
(CSMF) framework, which is applicable to surveys that suffer significantly from
sample selection effects. The clustering measurements, which are not sensitive
to the random sampling (missing fraction) of galaxies, are widely used to
constrain the stellar-halo mass relation (SHMR). By incorporating a missing
fraction (incompleteness) component into the CSMF model (ICSMF), we use the
incomplete stellar mass function and galaxy clustering to simultaneously
constrain the missing fractions and the SHMRs. Tests based on mock galaxy
catalogs with a few typical missing fraction models show that this method can
accurately recover the missing fraction and the galaxy SHMR, and hence provides
us reliable measurements of the galaxy stellar mass functions. We then apply it
to the Baryon Oscillation Spectroscopic Survey (BOSS) over the redshift range
of 0.1<z<0.8 for galaxies of $M_*>10^{11}M_\odot$. We find the sample
completeness for BOSS is over 80% at z<0.6, but decreases at higher redshifts
to about 30%. After taking these completeness factors into account, we provide
accurate measurements of the stellar mass functions for galaxies with
$10^{11}M_\odot<M_*<10^{12}M_\odot$, as well as the SHMRs, over the redshift
range 0.1<z<0.8 in this largest galaxy redshift survey.
