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Title: Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models
Author(s): Freise, Fritjof
Gaffke, NorbertLook up in the Integrated Authority File of the German National Library
Schwabe, RainerLook up in the Integrated Authority File of the German National Library
Issue Date: 2021
Type: Article
Language: English
URN: urn:nbn:de:gbv:ma9:1-1981185920-1032713
Subjects: Approximate design
Adaptive estimation
Strong consistency
Asymptotic normality
Generalized linear model
Abstract: 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.
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Sponsor/Funder: Projekt DEAL 2021
Journal Title: Metrika
Publisher: Springer
Publisher Place: Berlin
Volume: 84
Original Publication: 10.1007/s00184-020-00803-0
Page Start: 851
Page End: 874
Appears in Collections:Fakultät für Mathematik (OA)

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