杨刘.无重复因析试验中一种估计散度效应的方法[J].数学研究及应用,2015,35(5):581~590
无重复因析试验中一种估计散度效应的方法
A Method for Estimating Dispersion Effects in Unreplicated Two-level Factorial Experiments
投稿时间:2014-05-28  最后修改时间:2015-07-08
DOI:10.3770/j.issn:2095-2651.2015.05.011
中文关键词:  散度效应  无重复因析试验  均方误差
英文关键词:dispersion effects  unreplicated factorial experiments  mean square errors
基金项目:
作者单位
杨刘 山西财经大学应用数学学院, 山西 太原 030006 
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中文摘要:
      自从Box和Meyer首次提出无重复因析试验中散度效应的识别和估计问题, 各种散度效应的估计方法(包括迭代和非迭代)被提出. 特别地, Brenneman 和Nair 给出了这些方法的一个综述, 并且他们验证了改进的Harvey方法优于其它的方法.本文中对于对数线性模型, 一个基于多个位置模型残差平均的非迭代的散度效应估计方法在模型选择阶段被提出. 在大多数的模拟实验模型中, 本文方法具有比MH方法更小的均方误差, 且它可以应用于MH方法不适用的0或小的绝对残差情形. 我们也考虑了这个估计的理论性质, 并进行了实例分析.
英文摘要:
      Since the paper of Box and Meyer who first considered the identification and estimation of dispersion effects from unreplicated factorial experiments, various different methods (both iterative and non-iterative) have been proposed for estimating dispersion effects. An overview of various methods was given by Brenneman and Nair and they showed that the modified Harvey (MH) method is better than other methods. For a log-linear or multiplicative model, a non-iterative estimation method of dispersion effects based on residuals averaging from multiple location effect models is proposed in model selection stage, which has been shown smaller Mean Square Errors (MSE) than the MH method in majority of simulated models. And it can apply to the situations with zero or small absolute residuals, but the MH method will be failure. The properties of this estimator are also considered. A real example is used to illustrate the results.
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