Nonparametric Multiple-Output Center-Outward Quantile Regression

• 成果类型: Article
• 署名作者: del Barrio, Eustasio; Sanz, Alberto Gonzalez; Hallin, Marc
• 署名单位: Universidad de Valladolid; Columbia University; Universite Libre de Bruxelles; Universite Libre de Bruxelles; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2366029
• 发表日期: 2025
• 页码: 818-832
• 关键词: depth; ranks

摘要

Building on recent measure-transportation-based concepts of multivariate quantiles, we are considering the problem of nonparametric multiple-output quantile regression. Our approach defines nested conditional center-outward quantile regression contours and regions with given conditional probability content, the graphs of which constitute nested center-outward quantile regression tubes with given unconditional probability content; these (conditional and unconditional) probability contents do not depend on the underlying distribution-an essential property of quantile concepts. Empirical counterparts of these concepts are constructed, yielding interpretable empirical contours, regions, and tubes which are shown to consistently reconstruct (in the Pompeiu-Hausdorff topology) their population versions. Our method is entirely nonparametric and performs well in simulations-with possible heteroscedasticity and nonlinear trends. Its potential as a data-analytic tool is illustrated on some real datasets. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.