Optimal Moments for the Analysis of Peculiar Velocity Surveys

We present a new method for the analysis of peculiar velocity surveys that removes contributions to velocities from small scale, nonlinear velocity modes while retaining information about large-scale motions. Our method utilizes Karhunen-Loève methods of data compression to construct a set of moments out of the velocities that are minimally sensitive to small-scale power. The set of moments are then used in a likelihood analysis. We develop criteria for the selection of moments, as well as a statistic to quantify the overall sensitivity of a set of moments to small-scale power. Although we discuss our method in the context of peculiar velocity surveys, it may also prove useful in other situations where data filtering is required.