EFFICIENT FUNCTIONAL LASSO KERNEL SMOOTHING FOR HIGH-DIMENSIONAL ADDITIVE REGRESSION

• 成果类型: Article
• 署名作者: Lee, Eun Ryung; Park, Seyoung; Mammen, Enno; Park, Byeong U.
• 署名单位: Sungkyunkwan University (SKKU); Yonsei University; Ruprecht Karls University Heidelberg; Seoul National University (SNU)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2415
• 发表日期: 2024
• 页码: 1741-1773
• 关键词: Nonparametric regression; asymptotic properties; quantile regression; selection; variables; identification; CONVERGENCE; markers; models; rates

摘要

Smooth backfitting has been proposed and proved as a powerful nonparametric estimation technique for additive regression models in various settings. Existing studies are restricted to cases with a moderate number of covariates and are not directly applicable to high dimensional settings. In this paper, we develop new kernel estimators based on the idea of smooth backfitting for high dimensional additive models. We introduce a novel penalization scheme, combining the idea of functional Lasso with the smooth backfitting technique. We investigate the theoretical properties of the functional Lasso smooth backfitting estimation. For the implementation of the proposed method, we devise a simple iterative algorithm where the iteration is defined by a truncated projection operator. The algorithm has only an additional thresholding operator over the projection-based iteration of the smooth backfitting algorithm. We further present a debiased version of the proposed estimator with implementation details, and investigate its theoretical properties for statistical inference. We demonstrate the finite sample performance of the methods via simulation and real data analysis.