$k$维球上一类非线性模型的局部$D$ -最优设计及其在logit和probit模型中的应用
Locally $D$-optimal Designs for a Wider Class of Non-linear Models on the $k$-dimensional Ball with applications to logit and probit models
摘要：
在本文中，我们将Radloff和Schwabe（2018）的结果扩展到更广泛的一类非线性多元回归模型，这些结果可以应用于泊松回归，负二项回归和删失比例风险模型。这包括具有logit和probit链接的二进制响应模型。对于这类模型，当设计区域是一个$k$维球时，我们得到（局部）$D$ -最优设计.对于相应的结构，我们利用的概念，不变性和等方差的最优设计的背景下，在我们以前的文件。与前面的结果相反，设计不一定在所有情况下都是精确设计。相反，近似的设计可以出现。这些结果可以推广到任意椭球设计区域。
英文摘要：
In this paper we extend the results of Radloff and Schwabe (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 other. 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.
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