Unified Robust Multivariate Analysis Including High-Dimensional Testing Based on Scaler Scale Analysis

摘要基于尺度分析的统一鲁棒多变量分析包括高维测试Kesar Singh本文的目标是建立一个基于尺度曲线概念的多参数测试的通用框架。与传统的方差-协方差矩阵相比，用比例曲线测量分布的规模有两个明显的优点：1)它提供了一个标量度量，因此比复杂矩阵度量更容易掌握其大小；ii)比例曲线是平面上的简单曲线，无论数据的维数有多高，该曲线都易于可视化和解释。该方法所提出的检验是完全非参数的、鲁棒的；考虑的参数范围从标准参数到涉及基因表达、天文统计和各种功能数据的高维参数。它通过易于读取的刻度带图形来完成高度复杂的测试任务。这种基于比例曲线的方法可以很容易地被所有统计从业者理解和实施。本建议中发展的方法将大大扩大尺度曲线和经典多元统计分析的应用，同时降低技术复杂性的水平。该提案的进展将进一步推动整个统计学学科，并促进遗传学和风险管理等领域的许多实际应用。出于教育目的，本研究活动将使学生学习现代统计技术，如稳健的多变量分析、自举法、基因表达数据分析等。通过这个项目，他们既可以获得理论研究技能，也可以获得实际数据的实践经验。这样的训练对于学生将来成为有贡献的统计学家是必不可少的。

AbstractUnified Robust Multivariate Analysis Including High-Dimensional Testing Based on Scaler Scale Analysis Kesar Singh The goal of this proposal is to develop a general framework for multiparameter testing based on the concept of scale curves. Using a scale curve to measure the scale of a distribution, in comparison with the traditional variance-covariance matrix, has two distinct advantages: i) it provides a scalar measure and thus easier to grasp its magnitude than the complex matrix measure; and ii) the scale curve is a simple curve on the plane no matter how high the dimension of the data, and this curve can be easily visualized and interpreted. The tests proposed in this proposal are completely nonparametric and robust; and the parameters considered range from the standard ones to high-dimensional parameters pertaining to gene expression, astro-statistical and various functional data. It accomplishes the highly complex testing tasks through easy to read figures of scale bands. This scale curve based methodology can be easily comprehensible and implementable by all practitioners of statistics. The methodology developed in this proposal will broaden substantially the application of scale curves and classical multivariate statistical analysis, while bringing down the level of technical complexities. Progress from this proposal should further the statistics discipline as a whole, and facilitate many practical applications in domains such as genetics, and risk management. For the educational purposes, the proposed research activities will allow the student to learn about modern statistics techniques such as robust multivariate analysis, the bootstrap, analysis of gene expression data, etc. Through this project, they can acquire both theoretical research skills and hands-on experience with real life data. Such training is essential for student to become contributing statisticians in the future.