  We explore a variety of statistics of clusters selected with cosmic shear
measurement by utilizing both analytic models and large numerical simulations.
We first develop a halo model to predict the abundance and the clustering of
weak lensing selected clusters. Observational effects such as galaxy shape
noise are included in our model. We then generate realistic mock weak lensing
catalogs to test the accuracy of our analytic model. To this end, we perform
full-sky ray-tracing simulations that allow us to have multiple realizations of
a large continuous area. We model the masked regions on the sky using the
actual positions of bright stars, and generate 200 mock weak lensing catalogs
with sky coverage of ~1000 squared degrees. We show that our theoretical model
agrees well with the ensemble average of statistics and their covariances
calculated directly from the mock catalogues. With a typical selection
threshold, ignoring shape noise correction causes overestimation of the
clustering of weak lensing selected clusters with a level of about 10%, and
shape noise correction boosts the cluster abundance by a factor of a few. We
calculate the cross-covariances using the halo model with accounting for the
effective reduction of the survey area due to masks. The covariance of the
cosmic shear auto power spectrum is affected by the mode-coupling effect that
originates from sky masking. Our model and the results can be readily used for
cosmological analysis with ongoing and future weak lensing surveys.
