Confidence regions for the location of response surface optima: the R package OptimaRegion
Confidence regions for the location of response surface optima: the R package OptimaRegion
复制标题
DOI：
10.1080/03610918.2020.1823412
复制
发表时间：
2020-09-29
影响因子：
0.9
通讯作者：
Rapkin, James
中科院分区：
文献类型：
--
作者：
del Castillo, Enrique;Chen, Peng;Rapkin, James
对最优值（全局最大值或最小值）位置的统计推断是响应曲面方法领域的主要目标之一，在工程和科学中有许多应用。虽然存在用于计算最优值位置上的置信区域的先前方法，但这些方法是基于正态分布假设的线性模型，并且没有具体解决与保证全局最优性相关的困难。本文描述了响应面模型全局最优值位置置信域的计算方法。该方法是基于自举和Tukey的数据深度，因此，它们的性能不依赖于分布的假设影响响应的错误。一个R语言的实现，包OptimaRegion，描述。支持参数（最多5个协变量的二次和三次多项式）和非参数模型（2个协变量的薄板样条）。一个覆盖率分析，展示了质量的区域发现。该软件包还包含一个R实现的Gloptipoly算法的全局优化多项式响应的界限。
Statistical inference on the location of the optima (global maxima or minima) is one of the main goals in the area of Response Surface Methodology, with many applications in engineering and science. While there exist previous methods for computing confidence regions on the location of optima, these are for linear models based on a Normal distribution assumption, and do not address specifically the difficulties associated with guaranteeing global optimality. This paper describes distribution-free methods for the computation of confidence regions on the location of the global optima of response surface models. The methods are based on bootstrapping and Tukey's data depth, and therefore their performance does not rely on distributional assumptions about the errors affecting the response. An R language implementation, the package OptimaRegion, is described. Both parametric (quadratic and cubic polynomials in up to 5 covariates) and nonparametric models (thin plate splines in 2 covariates) are supported. A coverage analysis is presented demonstrating the quality of the regions found. The package also contains an R implementation of the Gloptipoly algorithm for the global optimization of polynomial responses subject to bounds.