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Estimation and Uniform Inference in Sparse High-Dimensional Additive Models

Philipp Bach, Sven Klaassen, Jannis Kueck, Martin Spindler

arXiv 3 Apr 2020 · Statistics — Methodology · publishedJournal of Econometrics (2025) · 5 citations (OpenAlex)

arXiv:2004.01623 · PDF · DOI · OpenAlex · Extracted main text

Abstract

We develop a novel method to construct uniformly valid confidence bands for a nonparametric component $f_1$ in the sparse additive model $Y=f_1(X_1)+\ldots + f_p(X_p) + \varepsilon$ 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 $f_1$. 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.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Karl Gregory, Enno Mammen, and Martin Wahl (2021) Statistical inference in sparse high-dimensional additive models1.000173100%
2Junwei Lu, Mladen Kolar, and Han Liu (2019) Kernel meets sieve: Post-regularization confidence bands for sparse additive model0.874102100%
3Damian Kozbur (2020) Inference in additively separable models with a high-dimensional set of conditioning variables0.87482100%
4Aad W. Van der Vaart and Jon A. Wellner (1996) Weak convergence0.87452100%
5Alexandre Belloni, Victor Chernozukov, and Christian Hansen (2014) Inference on treatment effects after selection among high-dimensional controls0.81142100%
6Lukas Meier, Sara Van de Geer, and Peter Bühlmann (2009) High-dimensional additive modeling0.81142100%
7Victor Chernozhukov, Denis Chetverikov, Kengo Kato, et al (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors0.7373367%
8Victor Chernozhukov, Christian Hansen, and Martin Spindler (2015) hdm: High-Dimensional Metrics, 2015a self0.7373367%
9Damian Kozbur (2015) Inference in additively separable models with a high dimensional conditioning set0.69351100%
10Alexandre Belloni, Victor Chernozhukov, and Kengo Kato (2014) Uniform post-selection inference for least absolute deviation regression and other z-estimation problems0.64422100%

Showing the top 10 of 49 scored citations.