Statistical parallaxes and the fundamental distance scale

A maximum likelihood regression model for determining stellar distances using proper motion and radial velocity data is described. The method represents an improvement on techniques involving the derivation of secular and statistical parallaxes. In general, the implied mean absolute magnitude of any group of stars is inextricably linked with estimates of the group's overall kinematic properties, e.g. solar motion, velocity ellipsoid, etc. The validity of the regression model has been tested by applying it to sets of synthetic data and, in general, any bias on the mean absolute magnitude does not exceed 0.2 mag for reasonably sized samples, say 50 stars. The principal axes of the velocity ellipsoid and the intrinsic dispersion of absolute magnitude are, however, susceptible to some bias under certain circumstances. (author)