Functional approach to the asymptotic normality of the non-linear least squares estimator

Abstract

The derivation of the asymptotic normality LSE's under univariate non-linear regression models is presented based on the weak convergence of the natural random field generated by the sum of squared residuals. Some examples, showing that neglecting the condition of uniform convergence leads to serious errors are presented. This approach is analogous to that of Le Cam's for the case of a known smooth family of distributions.