Partially Linear Additive Regression with a General Hilbertian Response

• 成果类型: Article
• 署名作者: Cho, Sungho; Jeon, Jeong Min; Kim, Dongwoo; Yu, Kyusang; Park, Byeong U. U.
• 署名单位: Seoul National University (SNU); KU Leuven; University of Namur; Konkuk University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2149407
• 发表日期: 2024
• 页码: 942-956
• 关键词: directed acyclic graphs; selection; networks; likelihood; CONVERGENCE; latent; rates; MODEL

摘要

In this article we develop semiparametric regression techniques for fitting partially linear additive models. The methods are for a general Hilbert-space-valued response. They use a powerful technique of additive regression in profiling out the additive nonparametric components of the models, which necessarily involves additive regression of the nonadditive effects of covariates. We show that the estimators of the parametric components are root n-consistent and asymptotically Gaussian under weak conditions. We also prove that the estimators of the nonparametric components, which are random elements taking values in a space of Hilbert-space-valued maps, achieve the univariate rate of convergence regardless of the dimension of covariates. We present some numerical evidence for the success of the proposed method and discuss real data applications. Supplementary materials for this article are available online.