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We present a new class of estimators for computing small-scale power spectraand bispectra in configuration-space via weighted pair- and triple-counts, withno explicit use of Fourier transforms. Particle counts are truncated at$R_0\sim 100h^{-1}\,\mathrm{Mpc}$ via a continuous window function, which hasnegligible 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 withnumber density $n$. Our estimators are corrected for the survey geometry andhave neither self-count contributions nor discretization artifacts, making themideal for high-$k$ analysis. Unlike conventional Fourier transform basedapproaches, our algorithm becomes more efficient on small scales (since asmaller $R_0$ may be used), thus we may efficiently estimate spectra across$k$-space by coupling this method with standard techniques. We demonstrate theutility of the publicly available power spectrum algorithm by applying it toBOSS DR12 simulations to compute the high-$k$ power spectrum and itscovariance. In addition, we derive a theoretical rescaled-Gaussian covariancematrix, which incorporates the survey geometry and is found to be in goodagreement with that from mocks. Computing configuration- and Fourier-spacestatistics in the same manner allows us to consider joint analyses, which canplace stronger bounds on cosmological parameters; to this end we also discussthe cross-covariance between the two-point correlation function and thesmall-scale power spectrum.

Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space