(in Theory and Methods)
## Explicit Estimators of Parametric Functions in Nonlinear
Regression

A. Ronald Gallant

*Journal of the American Statistical Association*,
Vol. 75, No. 369. (Mar., 1980), pp. 182-193.

### Abstract

When repetitive estimations are to be made under field conditions
using data that follow a nonlinear regression law, a simple polynomial
function of the observations has considerable appeal as an estimator.
The polynomial estimator of finite degree with smallest average mean
squared error is found. Conditions are given such that as degree
increases it converges in probability to the Bayes estimator and its
average mean squared error converges to the lower bound of all square
integrable estimators. In an example, a linear estimator performs
better than the maximum likelihood estimator and nearly as well as the
Bayes estimator.
**Keywords: **Nonlinear regression, Explicit estimators, Bayes
estimator, Average mean squared error, Chemical kinetics, Compartment
analysis