The interplay of observational errors through numerical simulations   using the $1/V_{\rm max}$ method for magnitude and proper-motion samples of   local disk white dwarfs.}
  White dwarf cooling sequences provides a useful indicator of the evolutionary time scales involved in the chronometry and star formation history of the galactic disk and, for this reason, the luminosity function of white dwarfs has become a powerful tool for studies of the evolution and formation of the Milky Way.   We examine the faint-end ($M_V > +14$) behavior of the disk white dwarf luminosity function using the $1/V_{\rm max}$ method, but, for the first time, fully including the effects of realistic observational errors in the derived luminosity function.   We find that observational errors, mostly in the bolometric corrections and trigonometric parallaxes, play a major role in obliterating (real or artificial) small scale fluctuations in the luminosity function. A better estimator of the true luminosity function seems to be the median over simulations, rather than the mean. When using the latter, an age of 10 Gyr or older can not be ruled out from the sample of Leggett, Ruiz, and Bergeron (1998). 
Rene A. Mendez, Maria T. Ruiz