Extremal Depth for Functional Data and Applications

• 成果类型: Article
• 署名作者: Narisetty, Naveen N.; Nair, Vijayan N.
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1110033
• 发表日期: 2016
• 页码: 1705-1714
• 关键词: infinite-dimensional spaces; POLYNOMIAL REGRESSION; confidence bands; bootstrap; CLASSIFICATION; quantiles; notions

摘要

We propose a new notion called extremal depth (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme outlyingness!' ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: (a) the central region achieves the nominal (desired) simultaneous coverage probability; (b) there is a correspondence between ED-based (simultaneous) central regions and appropriate pointwise central regions; and (c) the method is resistant to certain classes of functional outliers. The article examines the performance of ED and compares it with other depth notions. Its usefulness is demonstrated through applications to constructing central regions, functional boxplots, outlier detection, and simultaneous confidence bands in regression problems. Supplementary materials for this article are available online.