  Modern large-scale surveys have allowed the identification of large numbers
of white dwarfs. However, these surveys are subject to complicated target
selection algorithms, which make it almost impossible to quantify to what
extent the observational biases affect the observed populations. The LAMOST
(Large Sky Area Multi-Object Fiber Spectroscopic Telescope) Spectroscopic
Survey of the Galactic anti-center (LSS-GAC) follows a well-defined set of
criteria for selecting targets for observations. This advantage over previous
surveys has been fully exploited here to identify a small yet
well-characterised magnitude-limited sample of hydrogen-rich (DA) white dwarfs.
We derive preliminary LSS-GAC DA white dwarf luminosity and mass functions. The
space density and average formation rate of DA white dwarfs we derive are
0.83+/-0.16 x 10^{-3} pc^{-3} and 5.42 +/- 0.08 x 10^{-13} pc^{-3} yr^{-1},
respectively. Additionally, using an existing Monte Carlo population synthesis
code we simulate the population of single DA white dwarfs in the Galactic
anti-center, under various assumptions. The synthetic populations are passed
through the LSS-GAC selection criteria, taking into account all possible
observational biases. This allows us to perform a meaningful comparison of the
observed and simulated distributions. We find that the LSS-GAC set of criteria
is highly efficient in selecting white dwarfs for spectroscopic observations
(80-85 per cent) and that, overall, our simulations reproduce well the observed
luminosity function. However, they fail at reproducing an excess of massive
white dwarfs present in the observed mass function. A plausible explanation for
this is that a sizable fraction of massive white dwarfs in the Galaxy are the
product of white dwarf-white dwarf mergers.
