Adaptive Analysis of Sparse Factorial Designs and Related Problems

稀疏因子设计的自适应分析及相关问题

• 批准号: 0308861
• 负责人: Weizhen Wang
• 金额: $ 8.71万
• 依托单位: Wright State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-15 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0308861&HistoricalAwards=false
• 关键词: Adaptive; Analysis; Sparse; Factorial; Designs

DMS-0308861Adaptive analysis of sparse factorial designs and related problemsWeizhen Wang and Daniel T. VossAbstractThe investigators study the statistical theory underlying control of error rates for adaptive analysis of sparse factorial designs. Considered are orthogonal and nonorthogonal saturated designs, nearly saturated designs, and supersaturated designs. Methods under consideration rely upon the presence of an adequate but unknown level of effect sparsity, for lack of an adequate variance estimator independent of the effect estimates, and adapt to the level of effect sparsity suggested by the data. Much of the difficulty and intrigue lies in the apparently circular nature of the required arguments, since relatively large effect estimates are in some sense adaptively set aside for variance estimation, then the resulting variance estimate is used to make inferences about the effects. Lack of an adequate independent variance estimator gives rise to a variety of problems that are important and technically challenging. The investigators bring to bear on these problems a geometric perspective and the rigor and perspective of the multiple comparisons field, seeking methods of inference that control error rate strongly, while using the data adaptively and efficiently.The investigators study the probabilistic foundations of data analysis for sophisticated experiments fundamental to the development and production of high-quality, low-cost products. Critical characteristics often depend in unknown ways on an unknown subset of a larger collection of variables or factors. The resulting necessity to study many factors simultaneously in small, economical experiments--essentially to learn a lot from but a little data--presents many statistical challenges. While great progress has been made in the development of designs or plans for conducting such experiments, fundamental problems concerning the corresponding data analysis remain. The investigators study the theoretical foundations for the analysis of data from such experiments, and consequently propose innovative methods of data analysis, justifying them mathematically. This entails seeking solutions to a variety of related problems in probability pertinent to the analysis of data from such factorial experiments. Results have direct applications in engineering product and process design and in statistical process control and improvement, enhancing efforts to achieve competitive economic advantage.

DMS-0308861稀疏析因设计的自适应分析及相关问题王维珍和丹尼尔·沃斯摘要研究人员研究稀疏析因设计自适应分析中错误率控制的统计理论。考虑了正交性和非正交性饱和设计、近饱和设计和过饱和设计。考虑中的方法依赖于适当但未知水平的效果稀疏性的存在，因为缺乏独立于效果估计的适当的方差估计器，并适应数据所建议的效果稀疏性水平。许多困难和诡计在于所需参数的明显循环性质，因为在某种意义上，相对较大的效应估计被自适应地留作方差估计，然后产生的方差估计被用来对影响进行推断。缺乏足够的独立方差估计导致了各种重要的和技术上具有挑战性的问题。研究人员将几何观点和多重比较领域的严谨和视角运用到这些问题上，寻求强有力地控制错误率的推理方法，同时自适应和高效地使用数据。研究人员研究复杂实验的数据分析的概率基础，这是开发和生产高质量、低成本产品的基础。关键特征通常以未知的方式依赖于更大的变量或因素集合中的未知子集。由此产生的在小型、经济的实验中同时研究许多因素的必要性--基本上是从很少的数据中学到很多东西--带来了许多统计学上的挑战。虽然在设计或计划进行这类实验方面取得了很大进展，但与相应的数据分析有关的基本问题仍然存在。研究人员研究了分析此类实验数据的理论基础，因此提出了数据分析的创新方法，并从数学上证明了这些方法的合理性。这需要在与此类析因实验的数据分析相关的概率中寻求各种相关问题的解决方案。结果直接应用于工程产品和过程设计以及统计过程控制和改进，加强努力以获得竞争经济优势。