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