Locally ϕp-optimal designs for generalized linear models with a single-variable quadratic polynomial predictor
Locally ϕp-optimal designs for generalized linear models with a single-variable quadratic polynomial predictor
复制标题
具有单变量二次多项式预测器的广义线性模型的局部 phip 最优设计
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
J. Stufken
中科院分区：
文献类型：
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作者：
H. P. Wu;J. Stufken
寻找广义线性模型的最优设计是一个具有挑战性的问题。最近的研究已经确定了广义线性模型的最优设计的结构，其中单个或多个不相关的解释变量在预测变量中显示为一阶项。我们考虑广义线性模型与一个单变量的二次多项式作为预测下一个流行的家庭的最优性准则。当设计区域不受限制时，我们的研究结果表明，最优设计可以在基于对称结构的小支撑的设计子类中找到。我们表明，相同的结论持有一定的限制设计区域，但在其他情况下，可能要考虑一个更大的子类。此外，我们推导出一些D-最优设计的显式表达式。
Finding optimal designs for generalized linear models is a challenging problem. Recent research has identified the structure of optimal designs for generalized linear models with single or multiple unrelated explanatory variables that appear as first-order terms in the predictor. We consider generalized linear models with a single-variable quadratic polynomial as the predictor under a popular family of optimality criteria. When the design region is unrestricted, our results establish that optimal designs can be found within a subclass of designs based on a small support with symmetric structure. We show that the same conclusion holds with certain restrictions on the design region, but in other cases a larger subclass may have to be considered. In addition, we derive explicit expressions for some D-optimal designs.