NONLINEAR-REGRESSION WITH VARIANCE-COMPONENTS

The nonlinear model with variance components, which combines a nonlinear model for the mean with additive random effects, is applicable to split-plot and nested experiments. We propose two methods of estimation for the parameters of the nonlinear model for the mean: (1) estimated generalized least squares (EGLS), and (2) maximum likelihood (MLE) by the method of scoring. Using a generalization of Klimko and Nelson's theorem on strong consistency of least squares estimators, it is possible to show that both the MLE and the EGLS estimators are strongly consistent, asymptotically normal, and asymptotically efficient.