Adaptive Analysis of Sparse Factorial Designs and Related Problems

稀疏析因设计的适应性分析及相关问题研究人员研究了稀疏析因设计自适应分析中误差率控制的统计理论。 考虑的是正交和非正交饱和设计、近饱和设计和过饱和设计。 考虑中的方法依赖于一个足够的，但未知水平的效果稀疏的存在，缺乏足够的方差估计独立的效果估计，并适应数据所建议的效果稀疏的水平。 大部分的困难和阴谋在于所需的参数显然是循环的性质，因为相对较大的效应估计在某种意义上是自适应地留出方差估计，然后得到的方差估计是用来推断的影响。 缺乏一个足够的独立方差估计引起了各种问题，是重要的和技术上的挑战。 研究人员从几何学的角度和多重比较领域的严格性和视角来研究这些问题，寻求能够有效控制错误率的推理方法，同时自适应地有效使用数据。研究人员研究数据分析的概率基础，为开发和生产高质量、低成本的产品提供基础。 关键特性通常以未知的方式取决于更大的变量或因素集合的未知子集。 由此产生的必要性，同时研究许多因素在小，经济的实验-基本上是从一个小的数据学习很多-提出了许多统计挑战。 虽然在进行这种实验的设计或计划的发展方面取得了很大进展，但有关相应数据分析的基本问题仍然存在。 研究人员研究从这些实验中分析数据的理论基础，从而提出创新的数据分析方法，并在数学上证明它们的合理性。 这需要寻求解决各种相关问题的概率相关的数据分析，从这样的析因实验。结果直接应用于工程产品和工艺设计，并在统计过程控制和改进，加强努力，以实现经济竞争优势。

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.