Depth for Curve Data and Applications

• 成果类型: Article
• 署名作者: de Micheaux, Pierre Lafaye; Mozharovskyi, Pavlo; Vimond, Myriam
• 署名单位: University of New South Wales Sydney; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1745815
• 发表日期: 2021
• 页码: 1881-1897
• 关键词: functional data; MULTIVARIATE; CLASSIFICATION; fiber; definition; statistics; quantiles; notions; shapes

摘要

In 1975, John W. Tukey defined statistical data depth as a function that determines the centrality of an arbitrary point with respect to a data cloud or to a probability measure. During the last decades, this seminal idea of data depth evolved into a powerful tool proving to be useful in various fields of science. Recently, extending the notion of data depth to the functional setting attracted a lot of attention among theoretical and applied statisticians. We go further and suggest a notion of data depth suitable for data represented as curves, or trajectories, which is independent of the parameterization. We show that our curve depth satisfies theoretical requirements of general depth functions that are meaningful for trajectories. We apply our methodology to diffusion tensor brain images and also to pattern recognition of handwritten digits and letters. for this article are available online.