  We present an improved method for calculating the parallel and perpendicular
velocity correlation functions directly from peculiar velocity surveys using
weighted maximum-likelihood estimators. A central feature of the new method is
the use of position-dependent weighting scheme that reduces the influence of
nearby galaxies, which are typically overrepresented relative to the more
distant galaxies in most surveys. We demonstrate that the correlation functions
calculated this way are less susceptible to biases due to our particular
location in the Universe, and thus are more easily comparable to linear theory
and between surveys. Our results suggest that the parallel velocity correlation
function is a promising cosmological probe, given that it provides a better
approximation of a Gaussian distribution than other velocity correlation
functions and that its bias is more easily minimized by weighting. Though the
position weighted parallel velocity correlation function increases the
statistical uncertainty, it decreases the cosmic variance and is expected to
provide more stable and tighter cosmological parameter constraints than other
correlation methods in conjunction with more precise velocity surveys in the
future.

Cosmology and Nongalactic Astrophysics