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Title: Equivariance and invariance for optimal designs in generalized linear models exemplified by a class of gamma models
Author(s): Idais, Osama
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:ma9:1-1981185920-1030014
Subjects: Optimal design
Maximin efficiency
Generalized linear model
Abstract: The main intention of the present work is to outline the concept of equivariance and invariance in the design of experiments for generalized linear models and to demonstrate its usefulness. In contrast with linear models, pairs of transformations have to be employed for generalized linear models. These transformations act simultaneously on the experimental settings and on the location parameters in the linear component. Then, the concept of equivariance provides a tool to transfer locally optimal designs from one experimental region to another when the nominal values of the parameters are changed accordingly. The stronger concept of invariance requires a whole group of equivariant transformations. It can be used to characterize optimal designs which reflect the symmetries resulting from the group actions. The general concepts are illustrated by models with gamma distributed response and a canonical link. There, for a given transformation of the experimental settings, the transformation of the parameters is not unique and may be chosen to be nonlinear in order to fully exploit the model structure. In this case, we can derive invariant maximin efficient designs for the Dand the IMSE-criterion.
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: Journal of statistical theory and practice
Publisher: Springer International Publishing
Publisher Place: Cham
Volume: 15
Original Publication: 10.1007/s42519-021-00221-z
Page Start: 1
Page End: 32
Appears in Collections:Fakultät für Mathematik (OA)

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