Explicit Estimators of Parametric Functions in Nonlinear

The possibility of employing explicitly defined functions of the observations as estimators of parametric functions in nonlinear regression analysis is explored. A general theory of best average mean square error estimation leading to explicit estimators is set forth. Such estimators are given a Bayesian interpretation as Fourier expansions of the estimator which minimizes expected posterior square error loss. In an example a linear function of the observations performs better than the maximum likelihood estimator of the parametric function of interest and nearly as well as the Bayes estimator according to the criterion of average square error loss.