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Kernel Meets Sieve: Post-Regularization Confidence Bands for Sparse Additive Model

Author

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  • Junwei Lu
  • Mladen Kolar
  • Han Liu

Abstract

We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the literature, the kernel regression and the spline method, and is of interest in its own right. Existing methods for fitting sparse additive model are primarily based on sieve estimators, while the literature on confidence bands for nonparametric models are primarily based upon kernel or local polynomial estimators. Our kernel-sieve hybrid estimator combines the best of both worlds and allows us to provide a simple procedure for constructing confidence bands in high-dimensional sparse additive models. We prove that the confidence bands are asymptotically honest by studying approximation with a Gaussian process. Thorough numerical results on both synthetic data and real-world neuroscience data are provided to demonstrate the efficacy of the theory. Supplementary materials for this article are available online.

Suggested Citation

  • Junwei Lu & Mladen Kolar & Han Liu, 2020. "Kernel Meets Sieve: Post-Regularization Confidence Bands for Sparse Additive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 2084-2099, December.
  • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:532:p:2084-2099
    DOI: 10.1080/01621459.2019.1689984
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    Cited by:

    1. Philipp Bach & Sven Klaassen & Jannis Kueck & Martin Spindler, 2020. "Estimation and Uniform Inference in Sparse High-Dimensional Additive Models," Papers 2004.01623, arXiv.org, revised Apr 2024.
    2. Qingliang Fan & Zijian Guo & Ziwei Mei & Cun-Hui Zhang, 2023. "Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity," Papers 2310.08063, arXiv.org, revised Jun 2024.
    3. Haofeng Wang & Hongxia Jin & Xuejun Jiang & Jingzhi Li, 2022. "Model Selection for High Dimensional Nonparametric Additive Models via Ridge Estimation," Mathematics, MDPI, vol. 10(23), pages 1-22, December.

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