Mass Functions, Luminosity Functions, and Completeness Measurements from
  Clustering Redshifts
  This paper presents stellar mass functions and i-band luminosity functions
for Sloan Digital Sky Survey (SDSS) galaxies at $i < 21$ using clustering
redshifts, from which we also compute targeting completeness measurements for
the Baryon Oscillation Spectroscopic Survey (BOSS). Clustering redshifts is a
method of obtaining the redshift distribution of a sample of galaxies with only
photometric information by measuring the angular crosscorrelation with a
spectroscopic sample in different redshift bins. We construct a spectroscopic
sample containing data from the BOSS + eBOSS surveys, allowing us to recover
redshift distributions from photometric data out to $z\simeq 2.5$. We produce
k-corrected i-band luminosity functions and stellar mass functions by applying
clustering redshifts to SDSS DR8 galaxies in small bins of colour and
magnitude. There is little evolution in the mass function between $0.2 < z <
0.8$, implying the most massive galaxies form most of their mass before $z =
0.8$. These mass functions are used to produce stellar mass completeness
estimates for the Baryon Oscillation Spectroscopic Survey (BOSS), giving a
stellar mass completeness of $80\%$ above $M_{\star} > 10^{11.4}$ between $0.2
< z < 0.7$, with completeness falling significantly at redshifts higher than
0.7, and at lower masses. Large photometric datasets will be available in the
near future (DECaLS, DES, Euclid), so this, and similar techniques will become
increasingly useful in order to fully utilise this data.
