Nonparametric and Robust Multivariate Analysis via Quantile Functions

通过分位数函数进行非参数和稳健的多元分析

• 批准号: 0103698
• 负责人: Robert Serfling
• 金额: $ 28.43万
• 依托单位: University of Texas at Dallas
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103698&HistoricalAwards=false
• 关键词: Nonparametric; Robust; Multivariate; Analysis; via

This project develops concepts, perspectives, and tools leading toward a conceptually well-founded theory and methodology of nonparametric and robust data analysis in arbitrary dimension. The general framework being developed includes extensions of the traditional tools of one-dimensional analysis as well as tools unique to the higher-dimensional context. A theory of "median oriented quantile functions" having probabilistic interpretations similar to univariate quantiles is being pursued. A central approach is based on statistical depth functions. A major secondary objective is to bring the depth-based approach to a definitive degree of completion. Topics receiving special focus include multivariate quantile functions, depth functions, vector-valued L-statistics, matrix-valued scale statistics, generalized quantile processes, and generalized L-statistics. Linearization techniques via functional representations are used. Overall, the project advances nonparametric and robust multivariate analysis using quantile methods and addresses a range of specific applications.As the scope of application of multivariate statistical modeling has widened, the treatment of multivariate probability distributions and data has become increasingly important and central. A great deal of univariate statistical analysis is carried out in terms of percentiles, which lend themselves easily to interpretation. The use of percentiles has become fundamental. This project extends such methodology to higher dimension, to support a coherent and meaningful "percentiles" approach to the analysis and interpretation of multivariate data. Users of multivariate statistics in diverse fields of application thus acquire a tool that is of fundamental importance and conceptually well understood.

该项目发展了概念、观点和工具，从而形成了一个概念上良好的理论和方法，用于任意维度的非参数和稳健数据分析。正在开发的总体框架包括传统一维分析工具的扩展，以及用于高维上下文的独特工具。一种具有类似于单变量分位数的概率解释的“面向中位数的分位数函数”理论正在被研究。一个中心方法是基于统计深度函数。第二个主要目标是使基于深度的方法达到确定的完井程度。特别关注的主题包括多元分位数函数、深度函数、向量值l统计、矩阵值尺度统计、广义分位数过程和广义l统计。通过函数表示使用线性化技术。总体而言，该项目使用分位数方法推进了非参数和稳健的多变量分析，并解决了一系列具体应用。随着多元统计建模应用范围的扩大，对多元概率分布和数据的处理变得越来越重要和核心。大量的单变量统计分析是用百分位数进行的，这使它们易于解释。百分位数的使用已经成为基础。本项目将这种方法扩展到更高的维度，以支持连贯和有意义的“百分位数”方法来分析和解释多变量数据。多元统计的用户在不同的应用领域，从而获得一个工具，是基本的重要性和概念上很好理解。