Estimation and Uniform Inference in Sparse High-Dimensional Additive Models
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| author | Bach, Philipp Klaassen, Sven Kueck, Jannis Spindler, Martin |
| author_facet | Bach, Philipp Klaassen, Sven Kueck, Jannis Spindler, Martin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_01623 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Estimation and Uniform Inference in Sparse High-Dimensional Additive Models Bach, Philipp Klaassen, Sven Kueck, Jannis Spindler, Martin Methodology Econometrics Machine Learning 62G08, 62-07 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. |
| title | Estimation and Uniform Inference in Sparse High-Dimensional Additive Models |
| topic | Methodology Econometrics Machine Learning 62G08, 62-07 |
| url | https://arxiv.org/abs/2004.01623 |