Efficient Fully Distribution-Free Center-Outward Rank Tests for Multiple-Output Regression and MANOVA

• 成果类型: Article
• 署名作者: Hallin, Marc; Hlubinka, Daniel; Hudecova, Sarka
• 署名单位: Universite Libre de Bruxelles; Universite Libre de Bruxelles; Charles University Prague
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2021921
• 发表日期: 2023
• 页码: 1923-1939
• 关键词: Asymptotic Normality; MULTIVARIATE; depth; interdirections; randomness; quantiles

摘要

Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions proposed so far is enjoying the combination of distribution-freeness and efficiency that makes rank-based inference a successful tool in the univariate setting. A concept of center-outward multivariate ranks and signs based on measure transportation ideas has been introduced recently. Center-outward ranks and signs are not only distribution-free but achieve in dimension d > 1 the (essential) maximal ancillarity property of traditional univariate ranks. In the present case, we show that fully distribution-free testing procedures based on center-outward ranks can achieve parametric efficiency. We establish the Hajek representation and asymptotic normality results required in the construction of such tests in multiple-output regression and MANOVA models. Simulations and an empirical study demonstrate the excellent performance of the proposed procedures.