Gaussian approximation for non-linearity parameter estimation in perturbed random fields on the sphere

Abstract

We develop a probabilistic framework for the asymptotic analysis of a bispectrum-based estimator of primordial non-Gaussianity for isotropic random fields on the sphere in the high-resolution regime. By reformulating the estimation problem as an ordinary least squares regression, we derive the asymptotic moments of the estimator. Combining these results with Stein-Malliavin techniques on Wiener chaos yields a quantitative Gaussian approximation with an explicit convergence rate in total variation distance. The analysis relies on sharp asymptotic estimates for the deterministic weights arising from spherical harmonic coupling coefficients. Numerical experiments illustrate the predicted scaling laws and provide qualitative evidence for the asymptotic Gaussian behavior.

31 pages, 2 figures