A Note on Asymptotics of Least Squares for Nonlinear Harmonic Regression

This note considers the least-squares estimator of a nonlinear regression problem where the regression function is a sum of sinusoids with unknown amplitudes and frequencies. It points out some gaps and flaws in the current literature that attempts to prove the consistency and asymptotic normality of the nonlinear least-squares estimator. It also provides a rigorous and complete proof of the consistency and asymptotic normality by closing these gaps.

Published as Asymptotics of Least Squares for Nonlinear Harmonic Regression