  The skew-spectrum statistic introduced by Munshi & Heavens (2010) has
recently been used in studies of non-Gaussianity from diverse cosmological data
sets including the detection of primary and secondary non-Gaussianity of Cosmic
Microwave Background (CMB) radiation. Extending previous work, focussed on
independent estimation, here we deal with the question of joint estimation of
multiple skew-spectra from the same or correlated data sets. We consider the
optimum skew-spectra for various models of primordial non-Gaussianity as well
as secondary bispectra that originate from the cross-correlation of secondaries
and lensing of CMB: coupling of lensing with the Integrated Sachs-Wolfe (ISW)
effect, coupling of lensing with thermal Sunyaev-Zeldovich (tSZ), as well as
from unresolved point-sources (PS). For joint estimation of various types of
non-Gaussianity, we use the PCA to construct the linear combinations of
amplitudes of various models of non-Gaussianity, e.g. $f^{\rm loc}_{\rm
NL},f^{\rm eq}_{\rm NL},f^{\rm ortho}_{\rm NL}$ that can be estimated from CMB
maps. Bias induced in the estimation of primordial non-Gaussianity due to
secondary non-Gaussianity is evaluated. The PCA approach allows one to infer
approximate (but generally accurate) constraints using CMB data sets on any
reasonably smooth model by use of a lookup table and performing a simple
computation. This principle is validated by computing constraints on the DBI
bispectrum using a PCA analysis of the standard templates.
