Mathematical Sciences: Statistical Inference Under PatternedAlternatives Based on the Principle of Isotonic Regression

这项研究处理的是关于假设的统计推断，在该假设中，参数向量包含在由序限制定义的锥并集中。当已知参数遵循某种模式时，自然会出现这样的约束。研究的目的是将用于序限制推理的保序回归理论推广到这一更一般的背景下。本文提出了三种具体的解决方案。第一个涉及修改用于计算向量的保序回归的算法。第二种是研究基于对比的检验统计量的分布特性，包括同时多重比较过程。这项对统计推断理论的研究是当前努力的主要内容，目的是创建在感兴趣的变量被排序时有效的统计数据。统计推断的当前技术状态假设变量是分类的或连续的。这项研究的目的是将统计学扩展到一大类没有严格理论的变量。

This research deals with statistical inference concerning hypotheses in which a vector of parameters is contained in a union of cones defined by order restrictions. Such constraints arise naturally when the parameters are known to follow a pattern. The aim of the research is to extend the theory of isotonic regression, which is used in order restricted inference, to this more general setting. Three specific approaches are proposed. The first involves modifying algorithms used for calculating the isotonic regression of a vector. The second is to investigate the distributional properties of test statistics based on contrasts, including a simultaneous multiple comparison procedure. This research in the theory of statistical inference is a major effort in a current thrust to create statistics that are valid when the variable of interest is ordered. The current state of the art in statistical inference assumes the variable to be categorial or continuous. This research aims to extend statistics to a large class of variables for which there is not a rigorous theory.