Multivariate Functional Halfspace Depth

• 成果类型: Article
• 署名作者: Claeskens, Gerda; Hubert, Mia; Slaets, Leen; Vakili, Kaveh
• 署名单位: KU Leuven; KU Leuven; European Organisation for Research & Treatment of Cancer
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.856795
• 发表日期: 2014
• 页码: 411-423
• 关键词: maximum depth; CLASSIFICATION; contours

摘要

This article defines and studies a depth for multivariate functional data. By the multivariate nature and by including a weight function, it acknowledges important characteristics of functional data, namely differences in the amount of local amplitude, shape, and phase variation. We study both population and finite sample versions. The multivariate sample of curves may include warping functions, derivatives, and integrals of the original curves for a better overall representation of the functional data via the depth. We present a simulation study and data examples that confirm the good performance of this depth function. Supplementary materials for this article are available online.