  We present a three-dimensional reconstruction of the velocity distribution of
nearby stars (<~ 100 pc) using a maximum likelihood density estimation
technique applied to the two-dimensional tangential velocities of stars. The
underlying distribution is modeled as a mixture of Gaussian components. The
algorithm reconstructs the error-deconvolved distribution function, even when
the individual stars have unique error and missing-data properties. We apply
this technique to the tangential velocity measurements from a kinematically
unbiased sample of 11,865 main sequence stars observed by the Hipparcos
satellite. We explore various methods for validating the complexity of the
resulting velocity distribution function, including criteria based on Bayesian
model selection and how accurately our reconstruction predicts the radial
velocities of a sample of stars from the Geneva-Copenhagen survey (GCS). Using
this very conservative external validation test based on the GCS, we find that
there is little evidence for structure in the distribution function beyond the
moving groups established prior to the Hipparcos mission. This is in sharp
contrast with internal tests performed here and in previous analyses, which
point consistently to maximal structure in the velocity distribution. We
quantify the information content of the radial velocity measurements and find
that the mean amount of new information gained from a radial velocity
measurement of a single star is significant. This argues for complementary
radial velocity surveys to upcoming astrometric surveys.
