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We give an overview over the usefulness of the concept of equivariance and invariance in the design of experiments for generalized linear models. In contrast to linear models here pairs of transformations have to be considered which act simultaneously on the experimental settings and on the location parameters in the linear component. Given the transformation of the experimental settings the parameter transformations are not unique and may be nonlinear to make further use of the model structure. The general concepts and results are illustrated by models with gamma distributed response. Locally optimal and maximin efficient design are obtained for the common D- and IMSE-criterion.
The gamma model is a generalized linear model for gamma-distributed outcomes. The model is widely applied in psychology, ecology or medicine. In this paper we focus on gamma models having a linear predictor without intercept. For a specific scenario
We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to derive ef
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the construction of ad
Additive models, as a natural generalization of linear regression, have played an important role in studying nonlinear relationships. Despite of a rich literature and many recent advances on the topic, the statistical inference problem in additive mo
Optimal design theory for nonlinear regression studies local optimality on a given design space. We identify designs for the Bradley--Terry paired comparison model with small undirected graphs and prove that every saturated D-optimal design is repres