Robust covariance estimation of galaxy-galaxy weak lensing: validation
  and limitation of jackknife covariance
  We develop a method to simulate galaxy-galaxy weak lensing by utilizing
all-sky, light-cone simulations and their inherent halo catalogs. Using the
mock catalog to study the error covariance matrix of galaxy-galaxy weak
lensing, we compare the full covariance with the "jackknife" (JK) covariance,
the method often used in the literature that estimates the covariance from the
resamples of the data itself. We show that there exists the variation of JK
covariance over realizations of mock lensing measurements, while the average JK
covariance over mocks can give a reasonably accurate estimation of the true
covariance up to separations comparable with the size of JK subregion. The
scatter in JK covariances is found to be $\sim10\%$ after we subtract the
lensing measurement around random points. However, the JK method tends to
underestimate the covariance at the larger separations, more increasingly for a
survey with a higher number density of source galaxies. We apply our method to
the the Sloan Digital Sky Survey (SDSS) data, and show that the 48 mock SDSS
catalogs nicely reproduce the signals and the JK covariance measured from the
real data. We then argue that the use of the accurate covariance, compared to
the JK covariance, allows us to use the lensing signals at large scales beyond
a size of the JK subregion, which contains cleaner cosmological information in
the linear regime.
