Least Squares Estimation for a Class of Non-Linear Models

摘要

A new method for determining least squares estimators for certain classes of non-linear models is discussed. The method is an extension of a variable projection method of Scolnik (1970), and involves the minimization of a modified functional. The feature of minimizing this modified functional is that for a certain class of non-linear models, called the constant coefficients case, only one half the parameters are involved initially. To find the estimators of the remaining parameters is straight forward and relatively easy. This new two-step procedure is shown to be equivalent to the over-all least squares procedure. The authors also discuss the case of a class of models called the variable coefficients class. For this case, the authors formulate a new algorithm for determining the estimators which make use of approximate confidence regions for the parameters. (Author)