# Estimation and Uniform Inference in Sparse High-Dimensional Additive Models

arXiv: https://arxiv.org/abs/2004.01623 · HTML: https://mlsanity.com/paper/2004.01623/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2020.

## Built on by (most cited first, 2 of 2)

- [Distributed Double Machine Learning with a Serverless Architecture](https://mlsanity.com/paper/2101.04025/) (2021)
- [Coordinated Double Machine Learning](https://mlsanity.com/paper/2206.00885/) (2022)

## Abstract (arXiv)

We develop a novel method to construct uniformly valid confidence bands for a nonparametric component f1 in the sparse additive model Y=f1(X1)+ldots + fp(Xp) + varepsilon 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 f1. 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.