Estimation and Uniform Inference in Sparse High-Dimensional Additive Models

Abstract

We develop a novel method to construct uniformly valid confidence bands for a nonparametric component $f_1$ in the sparse additive model $Y=f_1(X_1)+\dots +f_p(X_p)+\epsilon$ in a high-dimensional setting. Our method integrates sieve estimation into a high-dimensional Z-estimation framework, facilitating the construction of uniformly valid confidence bands for the target component $f_1$. To form these confidence bands, we employ a multiplier bootstrap procedure. Additionally, we provide rates for the uniform lasso estimation in high dimensions, which may be of independent interest. Through simulation studies, we demonstrate that our proposed method delivers reliable results in terms of estimation and coverage, even in small samples.

References in corpus (6)

• Simultaneous analysis of Lasso and Dantzig selector
• Component selection and smoothing in multivariate nonparametric regression
• Variable selection in nonparametric additive models
• High-dimensional additive modeling
• Sparsity in multiple kernel learning
• Two-step estimation of high dimensional additive models

Cited by in corpus (1)

• Distributed Double Machine Learning with a Serverless Architecture