Mathematical Sciences: Adaptive Distribution-free in Design of Experiments

这个项目的目的是提供一类类似于Hogg过程的自适应非参数程序，但对于更一般的情况，包括(I)在c-样本位置问题(C2)中对有序备选方案的检验，(Ii)在c-样本规模问题中对有序备选方案的检验，(Iii)在c-样本位置-尺度问题中的检验，(Iv)在单向布局、双向布局和多向布局方差分析(ANOVA)模型中的检验、估计和多重比较。此外，我们还将解决处理关系的实际问题。基于理论论证和一些广泛的蒙特卡罗研究，这些程序将优于(I)通常的(非自适应的)程序，即只处理等级和由此产生的统计量的程序，例如Wilcoxon，和(Ii)通常的参数程序(基于基本分布函数的正态假设)。该项目将拓宽知识，并探索与在方差分析(单变量和多变量)、多重比较、对比度估计等几个问题中研究自适应分布自由过程相关的新技术。它将加强现有的技术，并为未来相关领域的研究项目提供帮助。

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.