Nonparametric measure-transportation-based methods for directional data

• 成果类型: Article
• 署名作者: Hallin, M.; Liu, H.; Verdebout, T.
• 署名单位: Universite Libre de Bruxelles; Universite Libre de Bruxelles; Chinese Academy of Sciences; University of Science & Technology of China, CAS
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae026
• 发表日期: 2024
• 页码: 1172-1196
• 关键词: high-dimensional spheres; RIEMANNIAN-MANIFOLDS; UNIFORMITY; tests; distributions; quantiles; inference

摘要

This article proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile contours and regions and closed-form formulas under the classical assumption of rotational symmetry. The empirical versions of our distribution functions enjoy the expected Glivenko-Cantelli property of traditional distribution functions. They provide fully distribution-free concepts of ranks and signs and define data-driven systems of (curvilinear) parallels and (hyper)meridians. Based on this, we also construct a universally consistent test of uniformity and a class of fully distribution-free and universally consistent tests for directional MANOVA which, in simulations, outperform all their existing competitors. A real-data example involving the analysis of sunspots concludes the article.