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We investigate the statistical power of higher-order statistics andcross-correlation statistics to constrain the primordial non-Gaussianity fromthe imaging surveys. In particular, we consider the local-type primordial non-Gaussianity and discuss how well one can tightly constrain the higher-ordernon-Gaussian parameters ($g_{\rm NL}$ and $\tau_{\rm NL}$) as well as theleading order parameter $f_{\rm NL}$ from the halo/galaxy clustering and weakgravitational lensing measurements. Making use of a strong scale-dependentbehavior in the galaxy/halo clustering, Fisher matrix analysis reveals that thebispectra can break the degeneracy between non-Gaussian parameters ($f_{\rmNL}$, $g_{\rm NL}$ and $\tau_{\rm NL}$) and this will give simultaneousconstraints on those three parameters. The combination of cross-correlationstatistics further improves the constraints by factor of 2. As a result,upcoming imaging surveys like the Large Synoptic Survey Telescope have thepotential to improve the constraints on the primordial non-Gaussianity muchtighter than those obtained from the CMB measurement by Planck, giving us anopportunity to test the single-sourced consistency relation, $\tau_{\rm NL} \ge(36/25) f_{\rm NL}^2$.

Constraining higher-order parameters for primordial non-Gaussianities from power spectra and bispectra of imaging survey