Fast estimation of aperture mass statistics II: Detectability of higher
  order statistics in current and future surveys
  We explore an alternative method to the usual shear correlation function
approach for the estimation of aperture mass statistics in weak lensing survey
data. Our approach builds on the direct estimator method. In this paper, we
extend our analysis to statistics of arbitrary order and to the multiscale
aperture mass statistics. We show that there always exists a linear order
algorithm to retrieve any of these generalised aperture mass statistics from
shape catalogs when the direct estimator approach is adopted. We validate our
approach through application to a large number of Gaussian mock lensing surveys
where the true answer is known and we do this up to 10th order statistics. We
then apply our estimators to an ensemble of real-world mock catalogs obtained
from N-body simulations - the SLICS mocks, and show that one can expect to
retrieve detections of higher order clustering up to fourth order in a
KiDS-1000 like survey. We expect that these methods will be of most utility for
future wide-field surveys like Euclid and the Rubin Telescope.
