  Sky masking is unavoidable in wide-field weak lensing observations. We study
how masks affect the measurement of statistics of matter distribution probed by
weak gravitational lensing. We first use 1000 cosmological ray-tracing
simulations to examine in detail the impact of masked regions on the weak
lensing Minkowski Functionals (MFs). We consider actual sky masks used for a
Subaru Suprime-Cam imaging survey. The masks increase the variance of the
convergence field and the expected values of the MFs are biased. The bias then
affects the non-Gaussian signals induced by the gravitational growth of
structure. We then explore how masks affect cosmological parameter estimation.
We calculate the cumulative signal-to-noise ratio S/N for masked maps to study
the information content of lensing MFs. We show that the degradation of S/N for
masked maps is mainly determined by the effective survey area. We also perform
simple chi^2 analysis to show the impact of lensing MF bias due to masked
regions. Finally, we compare ray-tracing simulations with data from a Subaru 2
deg^2 survey in order to address if the observed lensing MFs are consistent
with those of the standard cosmology. The resulting chi^2/n_dof = 29.6/30 for
three combined MFs, obtained with the mask effects taken into account, suggests
that the observational data are indeed consistent with the standard LambdaCDM
model. We conclude that the lensing MFs are powerful probe of cosmology only if
mask effects are correctly taken into account.
