Center-Outward R-Estimation for Semiparametric VARMA Models

• 成果类型: Article
• 署名作者: Hallin, M.; La Vecchia, D.; Liu, H.
• 署名单位: Universite Libre de Bruxelles; University of Geneva; Lancaster University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1832501
• 发表日期: 2022
• 页码: 925-938
• 关键词: rank-based estimation; asymptotic linearity; optimal tests; regression; interdirections; EFFICIENCY; depth

摘要

We propose a new class of R-estimators for semiparametric VARMA models in which the innovation density plays the role of the nuisance parameter. Our estimators are based on the novel concepts of multivariate center-outward ranks and signs. We show that these concepts, combined with Le Cam's asymptotic theory of statistical experiments, yield a class of semiparametric estimation procedures, which are efficient (at a given reference density), root-n consistent, and asymptotically normal under a broad class of (possibly nonelliptical) actual innovation densities. No kernel density estimation is required to implement our procedures. AMonteCarlo comparative study of our R-estimators and other routinely applied competitors demonstrates the benefits of the novel methodology, in large and small sample. Proofs, computational aspects, and further numerical results are available in the supplementary materials. Supplementary materials for this article are available online.