Galaxy-galaxy lensing estimators and their covariance properties
  We study the covariance properties of real space correlation function
estimators -- primarily galaxy-shear correlations, or galaxy-galaxy lensing --
using SDSS data for both shear catalogs and lenses (specifically the BOSS LOWZ
sample). Using mock catalogs of lenses and sources, we disentangle the various
contributions to the covariance matrix and compare them with a simple
analytical model. We show that not subtracting the lensing measurement around
random points from the measurement around the lens sample is equivalent to
performing the measurement using the lens density field instead of the lens
over-density field. While the measurement using the lens density field is
unbiased (in the absence of systematics), its error is significantly larger due
to an additional term in the covariance. Therefore, this subtraction should be
performed regardless of its beneficial effects on systematics. Comparing the
error estimates from data and mocks for estimators that involve the
over-density, we find that the errors are dominated by the shape noise and lens
clustering, that empirically estimated covariances (jackknife and standard
deviation across mocks) are consistent with theoretical estimates, and that
both the connected parts of the 4-point function and the super-sample
covariance can be neglected for the current levels of noise. While the
trade-off between different terms in the covariance depends on the survey
configuration (area, source number density), the diagnostics that we use in
this work should be useful for future works to test their
empirically-determined covariances.
