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变量框架，并产生了强大的多变量分析工具集。然而，它在间距和分类方面的全部潜力尚未得到充分探索。在几个实际应用的激励下，研究者计划：1)开发基于DD （Depth-vs-Depth）图的非参数分类程序。这些程序被称为dd分类器，它们将与所谓的支持向量机程序进行比较；2)使用从数据深度得出的多变量间距：（2a）为功能或时间序列数据构建公差包络，（2b）开发一类多变量拟合优度检验。分类在所有科学领域都是一项重要的任务，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。运用数据深度的概念，研究者提出开发有效的分类程序，该程序可以自动产生用于分类目的的最佳分离力，并与高度校准的现有分类程序竞争。无论数据的维度如何，分类结果都可以很容易地在二维图中可视化。研究者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程序。特别是，研究者应用这些间距来开发跟踪多变量数据和一类多变量拟合优度测试的容差信封。她计划将拟议的容许范围应用于飞机着陆模式的监测，以确保着陆安全。她还计划将提出的分类应用于疾病鉴定。这些应用程序的动机是研究者正在进行的与联邦航空管理局和罗伯特伍德约翰逊医学院精神病学部门的合作研究项目。提议的项目涉及真实的数据库，非常适合学生和博士后参与。

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.