Estimating Covariance Matrices for Two- and Three-Point Correlation
  Function Moments in Arbitrary Survey Geometries
  We present configuration-space estimators for the auto- and cross-covariance
of two- and three-point correlation functions (2PCF and 3PCF) in general survey
geometries. These are derived in the Gaussian limit (setting higher-order
correlation functions to zero), but for arbitrary non-linear 2PCFs (which may
be estimated from the survey itself), with a shot-noise rescaling parameter
included to capture non-Gaussianity. We generalize previous approaches to
include Legendre moments via a geometry-correction function calibrated from
measured pair and triple counts. Making use of importance sampling and random
particle catalogs, we can estimate model covariances in fractions of the time
required to do so with mocks, obtaining estimates with negligible sampling
noise in $\sim 10$ ($\sim 100$) CPU-hours for the 2PCF (3PCF) auto-covariance.
We compare results to sample covariances from a suite of BOSS DR12 mocks and
find the matrices to be in good agreement, assuming a shot-noise rescaling
parameter of $1.03$ ($1.20$) for the 2PCF (3PCF). To obtain strongest
constraints on cosmological parameters we must use multiple statistics in
concert; having robust methods to measure their covariances at low
computational cost is thus of great relevance to upcoming surveys.
