An Unbiased Method of Modeling the Local Peculiar Velocity Field with
  Type Ia Supernovae
  We apply statistically rigorous methods of nonparametric risk estimation to
the problem of inferring the local peculiar velocity field from nearby
supernovae (SNIa). We use two nonparametric methods - Weighted Least Squares
(WLS) and Coefficient Unbiased (CU) - both of which employ spherical harmonics
to model the field and use the estimated risk to determine at which multipole
to truncate the series. We show that if the data are not drawn from a uniform
distribution or if there is power beyond the maximum multipole in the
regression, a bias is introduced on the coefficients using WLS. CU estimates
the coefficients without this bias by including the sampling density making the
coefficients more accurate but not necessarily modeling the velocity field more
accurately. After applying nonparametric risk estimation to SNIa data, we find
that there are not enough data at this time to measure power beyond the dipole.
The WLS Local Group bulk flow is moving at 538 +- 86 km/s towards (l,b) = (258
+- 10 deg, 36 +- 11 deg) and the CU bulk flow is moving at 446 +- 101 km/s
towards (l,b) = (273 +- 11 deg, 46 +- 8 deg). We find that the magnitude and
direction of these measurements are in agreement with each other and previous
results in the literature.
