Reparametrization of weakly nonlinear regression models with constraints (Q2826339)

The author deals with general nonlinear regression models, in which the parameters of expectation are subject to a system of possibly nonlinear constraints. The focus here is on estimation. The author re-expresses the Bates and Watts curvature defined in terms of the second derivatives of the expectation function as well as of the nonlinear constraints function. There are two types of constraints considered here: the so-called type I constraints, which impose restrictions on the vector parameter of expectation only, and the type II constraints, which involve additional unknown vector parameters. The author reparametrizes and linearizes the model, in which then he shows closed forms for estimates of bias as well as covariance matrices of estimators. The developments here are general, without assuming normal distribution of the response. The paper is rather technical and at places very hard to follow. However, an interested reader my find the results helpful for further investigation, such as the construction of test statistic or confidence regions for parameters of interest.