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

Constraining $f_{NL}$ using the Large-Scale Modulation of Small-Scale Statistics