Mathematical Sciences: Adaptive Distribution-free in Design of Experiments

数学科学：实验设计中的自适应无分布

• 批准号: 9631168
• 负责人: Shan Sun
• 金额: $ 1.8万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9631168&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Adaptive; Distribution; free

The purpose of this project is to provide a class of adaptive nonparametric procedures similar to Hogg's procedures, but for more general situations, including (I) testing for ordered alternatives in the c-sample location problem (c2), (ii) testing for ordered alternatives in the c-sample scale problem, (iii) testing in the c-sample location - scale problem, (iv) testing, estimation and multiple comparisons in the one-way layout, two-way layout and multi-way layout analysis of variance (ANOVA) models. In addition, we will resolve the practical problem of handling ties. Based on the theoretical arguments as well as some extensive Monte Carlo studies, the supremacy of the procedures over (I) the usual (non-adaptive) procedure of working only with the ranks and the resulting statistics, such as Wilcoxon, and (ii) the usual parametric procedure (based on the assumption of normality of the underlying distribution function) will be established. This project will broaden the knowledge and explore new techniques related to the study of the adaptive distribution free procedures in several problems in the analysis of variance (univariate as well as multivariate), multiple comparisons, estimation of contrasts, among others. It will enhance the existing techniques and assist the future research projects in the related fields.

本项目的目的是提供一类类似于Hogg过程的自适应非参数过程，但适用于更一般的情况，包括(I) c-样本定位问题（c2）中有序替代方案的检验，（ii） c-样本尺度问题中有序替代方案的检验，（iii） c-样本定位尺度问题中的检验，（iv）单向布局中的检验、估计和多重比较。双向布局和多向布局方差分析模型。此外，我们将解决处理关系的实际问题。基于理论论证以及一些广泛的蒙特卡罗研究，这些过程优于(I)通常的（非自适应）过程，即只处理秩和结果统计，如Wilcoxon，以及（ii）通常的参数过程（基于底层分布函数的正态性假设）。本项目将在方差分析（单变量和多变量）、多重比较、对比估计等几个问题中，拓宽与自适应无分布程序研究相关的知识和探索新技术。它将加强现有技术，并协助未来相关领域的研究项目。