The evolution of the galaxy stellar mass function over the last twelve
  billion years from a combination of ground-based and HST surveys
  We present a new determination of the galaxy stellar mass function (GSMF)
over the redshift interval $0.25 \leq z \leq 3.75$, derived from a combination
of ground-based and Hubble Space Telescope (HST) imaging surveys. Based on a
near-IR selected galaxy sample selected over a raw survey area of 3 deg$^{2}$
and spanning $\geq 4$ dex in stellar mass, we fit the GSMF with both single and
double Schechter functions, carefully accounting for Eddington bias to derive
both observed and intrinsic parameter values. We find that a double Schechter
function is a better fit to the GSMF at all redshifts, although the single and
double Schechter function fits are statistically indistinguishable by $z=3.25$.
We find no evidence for significant evolution in $M^{\star}$, with the
intrinsic value consistent with $\log_{10}(M^{\star} /
M_{\odot})=10.55\pm{0.1}$ over the full redshift range. Overall, our
determination of the GSMF is in good agreement with recent simulation results,
although differences persist at the highest stellar masses. Splitting our
sample according to location on the UVJ plane, we find that the star-forming
GSMF can be adequately described by a single Schechter function over the full
redshift range, and has not evolved significantly since $z\simeq 2.5$. In
contrast, both the normalization and functional form of the passive GSMF
evolves dramatically with redshift, switching from a single to a double
Schechter function at $z \leq 1.5$. As a result, we find that while passive
galaxies dominate the integrated stellar-mass density at $z \leq 0.75$, they
only contribute $\lesssim 10$ per cent by $z\simeq 3$. Finally, we provide a
simple parameterization that provides an accurate estimate of the GSMF, both
observed and intrinsic, at any redshift within the range $0 \leq z \leq 4$.
