ADDITIVE REGRESSION FOR NON-EUCLIDEAN RESPONSES AND PREDICTORS

• 成果类型: Article
• 署名作者: Jeon, Jeong Min; Park, Byeong U.; Van Keilegom, Ingrid
• 署名单位: KU Leuven; Seoul National University (SNU)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2048
• 发表日期: 2021
• 页码: 2611-2641
• 关键词: kernel density-estimation; errors-in-variables; Nonparametric Regression; models; MANIFOLDS

摘要

Additive regression is studied in a very general setting where both the response and predictors are allowed to be non-Euclidean. The response takes values in a general separable Hilbert space, whereas the predictors take values in general semimetric spaces, which covers a very wide range of nonstandard response variables and predictors. A general framework of estimating additive models is presented for semimetric space-valued predictors. In particular, full details of implementation and the corresponding theory are given for predictors taking values in Hilbert spaces and/or Riemannian manifolds. The existence of the estimators, convergence of a backfitting algorithm, rates of convergence and asymptotic distributions of the estimators are discussed. The finite sample performance of the estimators is investigated by means of two simulation studies. Finally, three data sets covering several types of non-Euclidean data are analyzed to illustrate the usefulness of the proposed general approach.