  A convincing detection of primordial non-Gaussianity in the cosmic background
radiation (CMB) is essential to probe the physics of the early universe. Since
a single statistical estimator can hardly be suitable to detect the various
possible forms of non-Gaussianity, it is important to employ different
statistical indicators to study non-Gaussianity of CMB. This has motivated the
proposal of a number statistical tools, including two large-angle indicators
based on skewness and kurtosis of spherical caps of CMB sky-sphere. Although
suitable to detect fairly large non-Gaussianity they are unable to detect
non-Gaussianity within the Planck bounds, and exhibit power spectra with
undesirable oscillation pattern. Here we use several thousands simulated CMB
maps to examine interrelated problems regarding advances of these spherical
patches procedures. We examine whether a change in the choice of the patches
could enhance the sensitivity of the procedures well enough to detect
large-angle non-Gaussianity within the Planck bounds. To this end, a new
statistical procedure with non-overlapping cells is proposed and its capability
is established. We also study whether this new procedure is capable to smooth
out the undesirable oscillation pattern in the skewness and kurtosis power
spectra of the spherical caps procedure. We show that the new procedure solves
this problem, making clear this unexpected power spectra pattern does not have
a physical origin, but rather presumably arises from the overlapping obtained
with the spherical caps approach. Finally, we make a comparative analysis of
this new statistical procedure with the spherical caps routine, determine their
lower bounds for non-Gaussianity detection, and make apparent their relative
strength and sensitivity.
