In this paper we extend the results of Radloff and Schwabe (arXiv:1806.00275, 2018), which could be applied for example to Poisson regression, negative binomial regression and proportional hazard models with censoring, to a wider class of non-linear multiple regression models. This includes the binary response models with logit and probit link besides others. For this class of models we derive (locally) D-optimal designs when the design region is a k-dimensional ball. For the corresponding construction we make use of the concept of invariance and equivariance in the context of optimal designs as in our previous paper. In contrast to the former results the designs will not necessarily be exact designs in all cases. Instead approximate designs can appear. These results can be generalized to arbitrary ellipsoidal design regions.

中文翻译：

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k 维球上更广泛的非线性模型的局部 D 最优设计

在本文中，我们将 Radloff 和 Schwabe (arXiv:1806.00275, 2018) 的结果扩展到更广泛的非线性多元回归模型，这些结果可应用于泊松回归、负二项式回归和带删失的比例风险模型等. 除了其他模型之外，这还包括带有 logit 和 probit 链接的二元响应模型。对于此类模型，当设计区域是 k 维球时，我们推导出（局部）D 最优设计。对于相应的构造，我们在上一篇论文中在优化设计的上下文中使用了不变性和等方差的概念。与之前的结果相反，设计不一定在所有情况下都是精确的设计。相反，可能会出现近似设计。这些结果可以推广到任意椭球设计区域。