Data Depth for Nonparametric Multivariate Analysis: Goodness-of-Fit Tests Based on Spacings, Classification, and A Coherent Framework for Data Depth

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。先进的计算和数据采集技术使得在许多领域收集大型多元数据集成为可能。高效的多元统计分析工具，这样的数据集是非常抢手的。在现有的多变量分析方法中，基于数据深度的方法由于其高度理想的非参数性质而受到了广泛关注。本文沿着数据深度这一主题进一步展开，提出了非参数多元推理的三个新的研究项目：（1）发展一类新的基于多元间距的多元拟合优度检验，（2）引入一种新的基于DD图的非参数分类算法，（3）提出一种新的基于DD图的非参数分类算法，（4）提出一种新的基于DD图的非参数分类算法。（3）扩展数据深度的所有概念的一般框架，并开发适合于分析从非连续分布中提取的数据的新数据深度。该提案解决了理论多元统计中的重要问题，这些问题在实践中有广泛的应用。所有这三个研究方向都具有很强的竞争力，因为在这些方向上的任何新发展都将显着推进多元统计方法作为一个整体。拟议的研究还旨在提出许多有效的统计推断程序，可立即应用于许多领域，如医学，生物学，心理学，仅举几例。在生态学和环境科学的激励例子中阐述的建议。今后的出版物也将充分说明这些问题，这应有助于促进统计与其他领域之间更多的学科间互动。

This award is funded under the American Recovery and Reinvestment Act of 2009 Public Law 111-5). Advanced computing and data acquisition technologies have made possible the gathering of large multivariate data sets in many fields. Efficient multivariate statistical analysis tools for such data sets are highly sought after. Among the existing multivariate analysis approaches, the one based on the data depth has received most attention recently, due to its highly desirable nonparametric nature. Expanding further along the theme of data depth, this proposal outlines three new research projects in nonparametric multivariate inference, namely: (1) to develop a new class of multivariate goodness-of-fit tests based on multivariate spacings; (2) to introduce a novel nonparametric classification algorithm using the so-called DD-plots; (3) to extend the general framework for all notions of data depth, and to develop new data depths which are suitable for analyzing data drawn from non-continuous distributions. The proposal addresses important problems in theoretical multivariate statistics, which have a wide range of applications in practice. All three research directions are highly competitive, since any new development in these directions will significantly advance multivariate statistical methodology as a whole. The proposed research also aims to bring forth many efficient statistical inference procedures with immediate applicability in many domains such as medicine, biology, psychology, just to name a few. Motivating examples in ecology and environmental sciences are elaborated in the proposal. They will also be illustrated fully in future publications, which should help foster more interdisciplinary interaction between statistics and other fields.