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程序的自适应非参数程序，但适用于更一般的情况，包括（I）c-样本位置问题（c2）中的有序替代品的测试，（ii）c-样本规模问题中的有序替代品的测试，（iii）c-样本位置-规模问题中的测试，（iv）测试，单因素、双因素和多因素方差分析模型中的估计和多重比较。 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，将建立程序优于（I）仅使用秩和所得统计量的通常（非自适应）程序（如Wilcoxon）和（ii）通常的参数程序（基于基础分布函数的正态性假设）。 本项目将拓宽知识，探索与方差分析（单变量和多变量），多重比较，对比估计等几个问题中的自适应分布自由程序研究相关的新技术。 它将加强现有的技术，并协助未来的研究项目在相关领域。

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.