  We implement a novel formalism to constrain primordial non-Gaussianity of the
local type from the large-scale modulation of the small-scale power spectrum.
Our approach combines information about primordial non-Gaussianity contained in
the squeezed bispectrum and the collapsed trispectrum of large-scale structure
together in a computationally amenable and consistent way, while avoiding the
need to model complicated covariances of higher $N$-point functions. This work
generalizes our recent work, which used a neural network estimate of local
power, to the more conventional local power spectrum statistics, and explores
using both matter field and halo catalogues from the Quijote simulations. We
find that higher $N$-point functions of the matter field can provide strong
constraints on $f_{NL}$, but higher $N$-point functions of the halo field, at
the halo density of Quijote, only marginally improve constraints from the
two-point function.
