Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models - Fritjof Freise; Norbert Gaffke; Rainer Schwabe (Metrika, 2021)
The paper continues the authors' work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares estimators under the adaptive Wynn algorithm is studied. Strong consistency and asymptotic normality are derived for two classes of nonlinear models: firstly, for the class of models satisfying a condition of `saturated identifiability', which was introduced by Pronzato~(Metrika 71:219–238, 2010); secondly, a class of generalized linear models. Further essential assumptions are compactness of the experimental region and of the parameter space together with some natural continuity assumptions. For asymptotic normality some further smoothness assumptions and asymptotic homoscedasticity of random errors are needed and the true parameter point is required to be an interior point of the parameter space.
Keywords: L05; F12; J02; 510; Approximate design; D-optimality; Adaptive estimation; Strong consistency; Asymptotic normality; Generalized linear model