Estimation and Uniform Inference in Sparse High-Dimensional Additive Models

Philipp Bach; Sven Klaassen; Jannis Kueck; Martin Spindler

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arXiv · 2004.01623

Estimation and Uniform Inference in Sparse High-Dimensional Additive Models

Philipp Bach·Sven Klaassen·Jannis Kueck·Martin Spindler

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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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Philipp Bach, Sven Klaassen, Jannis Kueck, Martin Spindler. 2020-04-03. Estimation and Uniform Inference in Sparse High-Dimensional Additive Models. https://arxiv.org/abs/2004.01623

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