The Effects of Adaptation on Inference for Non-Linear Regression Models with Normal Errors

Abstract: This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since the second stage design is determined by the observations at the first stage; the MLE maximizes the total likelihood. Differently from the most of the literature, the first stage sample size is small, and hence asymptotic approximation is used only in the second stage. It is proved that the MLE is consistent and that its asymptotic distribution is a specific Gaussian mixture, via stable convergence. Finally, a simulation study is provided in the case of a dose-response Emax model.