几个竞争回归模型的最优判别设计
Optimal discriminating designs for several competing regression models
摘要：
考虑了一类回归模型的最优判别设计的构造问题。我们研究了Atkinson和Fedorov [Biometrika 62（1975 a）289-303]提出的$T_p$ -最优性准则的一个版本。当两两比较的次数大于2时，最优设计的数值构造是非常困难和具有挑战性的。它表明，最优设计相对于这种类型的标准，可以通过求解（非线性）向量值逼近问题。我们使用的最佳逼近的一个特征，以开发一个有效的算法，用于确定最佳鉴别设计。新的程序与目前可用的方法相比，在几个数值例子中，我们证明了新的方法可以找到最佳的鉴别设计的情况下，目前可用的程序失败。
英文摘要：
The problem of constructing optimal discriminating designs for a class of regression models is considered. We investigate a version of the $T_p$-optimality criterion as introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 289-303]. The numerical construction of optimal designs is very hard and challenging, if the number of pairwise comparisons is larger than 2. It is demonstrated that optimal designs with respect to this type of criteria can be obtained by solving (nonlinear) vector-valued approximation problems. We use a characterization of the best approximations to develop an efficient algorithm for the determination of the optimal discriminating designs. The new procedure is compared with the currently available methods in several numerical examples, and we demonstrate that the new method can find optimal discriminating designs in situations where the currently available procedures fail.
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