Fast Estimators for Redshift-Space Clustering
  Redshift-space distortions in galaxy surveys happen along the radial
direction, breaking statistical translation invariance. We construct estimators
for radial distortions that, using only Fast Fourier Transforms (FFTs) of the
overdensity field multipoles for a given survey geometry, compute the power
spectrum monopole, quadrupole and hexadecapole, and generalize such estimators
to the bispectrum. Using realistic mock catalogs we compare the signal to noise
of two estimators for the power spectrum hexadecapole that require different
number of FFTs and measure the bispectrum monopole, quadrupole and
hexadecapole. The resulting algorithm is very efficient, e.g. for the BOSS
survey requires about three minutes for $\ell=0,2,4$ power spectra for scales
up to $k=0.3~h/$Mpc and about fifteen additional minutes for $\ell=0,2,4$
bispectra for all scales and triangle shapes up to $k=0.2~h/$Mpc on a single
core. The speed of these estimators is essential as it makes possible to
compute covariance matrices from large number of realizations of mock catalogs
with realistic survey characteristics, and paves the way for improved
constrains of gravity on cosmological scales, inflation and galaxy bias.
