A UNIFIED METHOD TO CALCULATE THE MOMENTS OF THE LEAST SQUARES ESTIMATORS IN NONLINEAR REGRESSION

A unified method and a set of regularity conditions are presented in this paper to calculate themoments of the least squares estimators, residuals, and fitting errors in nonlinear regression. The resultsgiven by Box, Clarke and other authors have been greatly improved and developed. The key point ofthe method is that we find a series of stochastic expansions related to the estimators. These expansionsconsist of curvature measures and independent standard normal random variables: therefore they areeasy to understand and to deal with from statistical and geometrical point of view.