Kernel Meets Sieve: Post-Regularization Confidence Bands for Sparse Additive Model

• 成果类型: Article
• 署名作者: Lu, Junwei; Kolar, Mladen; Liu, Han
• 署名单位: Harvard University; Harvard T.H. Chan School of Public Health; University of Chicago; Northwestern University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1689984
• 发表日期: 2020
• 页码: 2084-2099
• 关键词: deficit-hyperactivity disorder; variable selection; component selection; linear-regression; Optimal Rates; hypothesis; inference; CONVERGENCE; estimators; bootstrap

摘要

We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the literature, the kernel regression and the spline method, and is of interest in its own right. Existing methods for fitting sparse additive model are primarily based on sieve estimators, while the literature on confidence bands for nonparametric models are primarily based upon kernel or local polynomial estimators. Our kernel-sieve hybrid estimator combines the best of both worlds and allows us to provide a simple procedure for constructing confidence bands in high-dimensional sparse additive models. We prove that the confidence bands are asymptotically honest by studying approximation with a Gaussian process. Thorough numerical results on both synthetic data and real-world neuroscience data are provided to demonstrate the efficacy of the theory. for this article are available online.