Article

Testing the minimum variance method for estimating large-scale velocity moments

Monthly Notices of the Royal Astronomical Society (Impact Factor: 5.11). 12/2011; 424(4). DOI: 10.1111/j.1365-2966.2012.21345.x
Source: arXiv

ABSTRACT

The estimation and analysis of large-scale bulk flow moments of peculiar velocity surveys is complicated by non-spherical
survey geometry, the non-uniform sampling of the matter velocity field by the survey objects and the typically large measurement
errors of the measured line-of-sight velocities. Previously, we have developed an optimal ‘;minimum variance’ (MV) weighting
scheme for using peculiar velocity data to estimate bulk flow moments for idealized, dense and isotropic surveys with Gaussian
radial distributions, that avoids many of these complications. These moments are designed to be easy to interpret and are
comparable between surveys. In this paper, we test the robustness of our MV estimators using numerical simulations. Using
MV weights, we estimate the bulk flow moments for various mock catalogues extracted from the LasDamas and the Horizon Run
numerical simulations and compare these estimates to the moments calculated directly from the simulation boxes. We show that
the MV estimators are unbiased and negligibly affected by non-linear flows.

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    • "Further, [31] also shows the inconsistency of the MLE. Recently, a more consistent and, in fact, optimal estimation method – 1 – was introduced to address these problems, called the Minimum Variance (MV) method [39] [40], and was tested further by citation [48] (for a recent implementation of the MV method see [49] [50]). Various studies have indicated that the BF magnitudes fit Maxwellian distribution (e.g. "
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