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

Junwei Lu*, Mladen Kolar, Han Liu

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

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. Supplementary materials for this article are available online.

Original languageEnglish (US)
JournalJournal of the American Statistical Association
DOIs
StateAccepted/In press - Jan 1 2020

Keywords

  • Confidence band
  • Kernel method
  • Sieve estimator
  • Sparse additive model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Kernel Meets Sieve: Post-Regularization Confidence Bands for Sparse Additive Model'. Together they form a unique fingerprint.

  • Cite this