  The peculiar velocities of galaxies are an inherently valuable cosmological
probe, providing an unbiased estimate of the distribution of matter on scales
much larger than the depth of the survey. Much research interest has been
motivated by the high dipole moment of our local peculiar velocity field, which
suggests a large scale excess in the matter power spectrum, and can appear to
be in some tension with the LCDM model. We use a composite catalogue of 4,537
peculiar velocity measurements with a characteristic depth of 33 h-1 Mpc to
estimate the matter power spectrum. We compare the constraints with this
method, directly studying the full peculiar velocity catalogue, to results from
Macaulay et al. (2011), studying minimum variance moments of the velocity
field, as calculated by Watkins, Feldman & Hudson (2009) and Feldman, Watkins &
Hudson (2010). We find good agreement with the LCDM model on scales of k > 0.01
h Mpc-1. We find an excess of power on scales of k < 0.01 h Mpc-1, although
with a 1 sigma uncertainty which includes the LCDM model. We find that the
uncertainty in the excess at these scales is larger than an alternative result
studying only moments of the velocity field, which is due to the minimum
variance weights used to calculate the moments. At small scales, we are able to
clearly discriminate between linear and nonlinear clustering in simulated
peculiar velocity catalogues, and find some evidence (although less clear) for
linear clustering in the real peculiar velocity data.
