We present the kinematics of a sample of 398 DA white dwarfs from the SPY project (ESO SN Ia Progenitor surveY) and discuss kinematic criteria for distinguishing thin-disk, thick-disk, and halo populations. This is the largest homogeneous sample of white dwarfs for which 3D space motions have been determined. Since the percentage of old stars among white dwarfs is higher than among main-sequence stars, they are presumably valuable tools in studies of old populations, such as the halo and the thick disk. Radial velocities and spectroscopic distances were combined with our measurements of proper motions to derive 3D space motions. Galactic orbits were computed. Our kinematic criteria for assigning population membership were deduced from a sample of F and G stars, for which chemical criteria can be used to distinguish between a thin-disk, a thick-disk and a halo star. Our kinematic population classification scheme is based on the position in the U-V-velocity diagram, the position in the Jz-eccentricity diagram, and the Galactic orbit. We combined this with age information and found seven halo and 27 thick-disk white dwarfs in this brightness limited sample. Correspondingly 2% of the white dwarfs belong to the halo and 7% to the thick disk. The mass contribution of the thick-disk white dwarfs is found to be substantial, but is insufficient to account for the missing dark matter. (abbreviated)
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