Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in
  Configuration-Space
  We present a new class of estimators for computing small-scale power spectra
and bispectra in configuration-space via weighted pair- and triple-counts, with
no explicit use of Fourier transforms. Particle counts are truncated at
$R_0\sim 100h^{-1}\,\mathrm{Mpc}$ via a continuous window function, which has
negligible effect on the measured power spectrum multipoles at small scales.
This gives a power spectrum algorithm with complexity $\mathcal{O}(NnR_0^3)$
(or $\mathcal{O}(Nn^2R_0^6)$ for the bispectrum), measuring $N$ galaxies with
number density $n$. Our estimators are corrected for the survey geometry and
have neither self-count contributions nor discretization artifacts, making them
ideal for high-$k$ analysis. Unlike conventional Fourier transform based
approaches, our algorithm becomes more efficient on small scales (since a
smaller $R_0$ may be used), thus we may efficiently estimate spectra across
$k$-space by coupling this method with standard techniques. We demonstrate the
utility of the publicly available power spectrum algorithm by applying it to
BOSS DR12 simulations to compute the high-$k$ power spectrum and its
covariance. In addition, we derive a theoretical rescaled-Gaussian covariance
matrix, which incorporates the survey geometry and is found to be in good
agreement with that from mocks. Computing configuration- and Fourier-space
statistics in the same manner allows us to consider joint analyses, which can
place stronger bounds on cosmological parameters; to this end we also discuss
the cross-covariance between the two-point correlation function and the
small-scale power spectrum.
