Data Depth: Multivariate Spacings and DD-Classifiers for Nonparametric Multivariate Classification

数据深度提供了一个系统的非参数多元框架，并产生了一个强大的多元分析工具集。然而，其在间距和分类方面的全部潜力尚未得到充分探索。受几个真实的应用的启发，研究者计划：1）开发基于DD（深度对深度）图的非参数分类程序。这些过程被称为DD-分类器，并且它们将与所谓的支持向量机过程进行比较; 2）使用从数据深度导出的多变量间距来：（2a）构造函数或时间序列数据的容差包络;（2b）发展一类多元拟合优度检验。分类是所有科学领域中的一项重要任务，例如在考古调查中识别新物种或在医学研究中区分疾病类型。应用数据深度的概念，调查员建议开发有效的分类程序，它可以自动产生最佳的分类分离能力，并与高度校准的现有分类程序竞争。无论数据的维度如何，分类结果都可以在二维图中轻松可视化。调查员还介绍了多维数据分析的多元间距。 这些多变量间距应该具有广泛的实用性。特别是，研究人员应用这些间距来开发用于跟踪多变量数据的公差包络和一类多变量拟合优度检验。她计划将拟议的容限包络应用于飞机着陆模式的监测，并确保着陆安全。她还计划将拟议的分类应用于疾病识别。这些应用程序的动机是由调查员正在进行的合作研究项目与联邦航空管理局和罗伯特伍德约翰逊医学院精神病学系。拟议的项目涉及真实的数据库，非常适合吸引学生和博士后。

Data depth has provided a systematic nonparametric multivariate framework and given rise to a powerful multivariate analysis tool set. However, its full potential in spacings and classification is yet to be fully explored. Motivated by several real applications, the investigator plans to: 1) develop nonparametric classification procedures based on DD (Depth-vs-Depth) plots. These procedures are referred to as DD-classifiers, and they are to be compared with the so-called support vector machine procedures; 2) use the multivariate spacings derived from data depth to: (2a) construct tolerance envelopes for functional or time series data and (2b) develop a class of multivariate goodness-of-fit tests.Classification is is an important task in all scientific domains, such as identifying new species in archaeological investigations or distinguishing disease types in medical studies. Applying the notion of data depth, the investigator proposes to develop effective classification procedures, which can automatically yield the best separating power for classification purposes and compete well with the highly calibrated existing classification procedures. The classification outcomes can be easily visualized in a two-dimensional plot regardless of the dimension of the data. The investigator also introduces multivariate spacings for the analysis of multi-dimensional data. These multivariate spacings should have a wide range of utilities. In particular, the investigator applies these spacings to develop both tolerance envelopes for tracking multivariate data and a class of multivariate goodness-of-fit tests. She plans to apply the proposed tolerance envelope to the monitoring of aircraft landing patterns and to ensure landing safety. She also plans to apply the proposed classifications to disease identification. These applications are motivated by the investigator's ongoing collaborative research projects with the Federal Aviation Administration and the Department of Psychiatry of the Robert Wood Johnson Medical School. The proposed projects involve real databases and are ideally suited for engaging students and postdocs.