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.

本文继续作者的工作（Freise等人，关于具有非线性回归模型的自适应Wynn算法的具有单变量响应的广义线性模型中的自适应Wynn算法.arXiv：1907.02708，2019）。本文研究了在自适应Wynn算法下的自适应最小二乘估计的渐近性。两类非线性模型具有很强的一致性和渐近正态性：第一，对于满足“饱和可识别性”条件的模型，这是由Pronzato提出的（Metrika 71：219-238，2010）；其次是一类广义线性模型。其他必要的假设是实验区域和参数空间的紧凑性以及一些自然的连续性假设。