Maximum likelihood estimation of local stellar kinematics
  Context. Kinematical data such as the mean velocities and velocity
dispersions of stellar samples are useful tools to study galactic structure and
evolution. However, observational data are often incomplete (e.g., lacking the
radial component of the motion) and may have significant observational errors.
For example, the majority of faint stars observed with Gaia will not have their
radial velocities measured. Aims. Our aim is to formulate and test a new
maximum likelihood approach to estimating the kinematical parameters for a
local stellar sample when only the transverse velocities are known (from
parallaxes and proper motions). Methods. Numerical simulations using
synthetically generated data as well as real data (based on the
Geneva-Copenhagen survey) are used to investigate the statistical properties
(bias, precision) of the method, and to compare its performance with the much
simpler "projection method" described by Dehnen & Binney (1998). Results. The
maximum likelihood method gives more correct estimates of the dispersion when
observational errors are important, and guarantees a positive-definite
dispersion matrix, which is not always obtained with the projection method.
Possible extensions and improvements of the method are discussed.
