Confidence Sets for Optimal Factor Levels of a Response Surface
Confidence Sets for Optimal Factor Levels of a Response Surface
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DOI：
10.1111/biom.12500
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发表时间：
2016-12-01
期刊：
影响因子：
1.9
通讯作者：
Han, Yang
中科院分区：
文献类型：
--
作者：
Wan, Fang;Liu, Wei;Han, Yang
构建最优因子水平的置信集是响应曲面方法中的一个重要课题。在Wan等人（2015年）的研究中，对于给定区间内一元多项式函数的最大或最小点（即最优因子水平），已经给出了一个精确的（1 - α）置信集。在本文中，该方法已被扩展用于构建响应曲面最优因子水平的精确（1 - α）置信集。这种构建方法很容易应用于许多涉及二次函数的参数和半参数回归模型。在构建精确置信集的过程中，作为中间步骤，给出了一个保守的置信集。给出了两个例子来说明置信集的应用。置信集之间的比较表明，我们的精确置信集优于统计文献中唯一可用的其他能保证（1 - α）置信水平的置信集。
Construction of confidence sets for the optimal factor levels is an important topic in response surfaces methodology. In Wan et al. (2015), an exact (1 - alpha) confidence set has been provided for a maximum or minimum point (i.e., an optimal factor level) of a univariate polynomial function in a given interval. In this article, the method has been extended to construct an exact (1 - alpha) confidence set for the optimal factor levels of response surfaces. The construction method is readily applied to many parametric and semiparametric regression models involving a quadratic function. A conservative confidence set has been provided as an intermediate step in the construction of the exact confidence set. Two examples are given to illustrate the application of the confidence sets. The comparison between confidence sets indicates that our exact confidence set is better than the only other confidence set available in the statistical literature that guarantees the (1 - alpha) confidence level.