Construction and Applications of Simultaneous Confidence Bands for Linear Regression Models

线性回归模型联立置信带的构建及应用

• 批准号: EP/E046126/1
• 负责人: Wei Liu
• 金额: $ 1.47万
• 依托单位: University of Southampton
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2007
• 资助国家: 英国
• 起止时间: 2007 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FE046126%2F1
• 关键词: Construction; Applications; Simultaneous; Confidence; Bands

Regression analysis is one of the most commonly employed statistical techniques. It has applications in all scientific areas, such as engineering, physics, chemistry, biology, finance, and medicine. Simultaneous confidence bands for regression models can be used not only to assess the plausible range of a regression model but also to gain quantitative information about the possible differences between different regression models. So the methodology of simultaneous confidence bands is an integral part of regression analysis and has immediate applications to data analysis.The proposed research is to study the construction of optimal confidence band which provides the most accurate information about a regression model under certain recently proposed optimality criterion, and to study ways of constructing simultaneous confidence bands of exact 1-a level for assessing the all-contrast differences of several regression model under some very general setting.

回归分析是最常用的统计技术之一。它在所有科学领域都有应用，如工程、物理、化学、生物、金融和医学。回归模型的同时置信带不仅可以用来评估回归模型的合理范围，而且可以获得关于不同回归模型之间可能差异的定量信息。因此，同时置信带方法是回归分析的一个组成部分，并在数据分析中有着直接的应用，本研究旨在研究在最近提出的最优性准则下，最优置信带的构造，它提供了关于回归模型的最准确的信息，研究了在一般情况下，如何构造精确1-a水平的同时置信带，以估计几个回归模型的全对比差异。