MAXIMIN EFFICIENT DESIGNS FOR ESTIMATING NONLINEAR ASPECTS IN LINEAR-MODELS
MAXIMIN EFFICIENT DESIGNS FOR ESTIMATING NONLINEAR ASPECTS IN LINEAR-MODELS
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DOI：
10.1016/0378-3758(94)00042-t
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发表时间：
1995-03-01
影响因子：
0.9
通讯作者：
MULLER, CH
中科院分区：
文献类型：
--
作者：
MULLER, CH
为了估计线性模型的非线性方面，在给定所考虑的设计的支持并提供线性无关回归量的情况下，导出了最大有效设计。除了一般结果外，还给出了两个特殊结果，在简单条件下提供了最有效的设计。其中一个结果给出了使均匀设计效率最大化的一个简单条件。另一个结果处理两点支撑的设计。这些结果有许多应用。通过几个例子证明了这一点，包括估计二次响应函数的最大值和最大值的问题，线性校准问题，基于回归的比率估计问题以及估计附加因素的相对影响和两种处理的等效性问题。其中一些例子重复了文献中已经用直接方法得出的结果。最后简要讨论了结果在非线性模型中的应用。
For estimating a nonlinear aspect of a linear model maximin efficient designs art derived for the case that the support of the regarded designs is given and provides linearly independent regressors. Besides a general result two special results are presented, which provide maximin efficient designs under simple conditions. One of these results gives a simple condition so that the uniform design is maximin efficient. The other result deals with designs with a two-point support. These results have many applications. This is demonstrated by several examples including the problems of estimating the maximum point and the maximum value of quadratic response functions, the linear calibration problem, the problem of regression-based ratio estimation and the problems of estimating the relative effect of an additional factor and the equivalence of two treatments. Some of these examples repeat results which were already derived in the literature by straightforward methods. At last the application of the results to nonlinear models is shortly discussed.