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The Partial Linear Model in High Dimensions

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  • Patric Müller
  • Sara Geer

Abstract

type="main" xml:id="sjos12124-abs-0001"> Partial linear models have been widely used as flexible method for modelling linear components in conjunction with non-parametric ones. Despite the presence of the non-parametric part, the linear, parametric part can under certain conditions be estimated with parametric rate. In this paper, we consider a high-dimensional linear part. We show that it can be estimated with oracle rates, using the least absolute shrinkage and selection operator penalty for the linear part and a smoothness penalty for the nonparametric part.

Suggested Citation

  • Patric Müller & Sara Geer, 2015. "The Partial Linear Model in High Dimensions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 580-608, June.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:580-608
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    File URL: http://hdl.handle.net/10.1111/sjos.12124
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    References listed on IDEAS

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    1. A. Belloni & V. Chernozhukov & L. Wang, 2011. "Square-root lasso: pivotal recovery of sparse signals via conic programming," Biometrika, Biometrika Trust, vol. 98(4), pages 791-806.
    2. Lian, Heng, 2012. "Shrinkage estimation for identification of linear components in additive models," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 225-231.
    3. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    4. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    2. Qingliang Fan & Zijian Guo & Ziwei Mei & Cun-Hui Zhang, 2023. "Uniform Inference for Nonlinear Endogenous Treatment Effects with High-Dimensional Covariates," Papers 2310.08063, arXiv.org, revised Oct 2023.
    3. Zhang, Jun & Feng, Zhenghui & Peng, Heng, 2018. "Estimation and hypothesis test for partial linear multiplicative models," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 87-103.
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    5. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.
    6. Wang, Yue & Zhou, Yan & Li, Rui & Lian, Heng, 2022. "Sparse high-dimensional semi-nonparametric quantile regression in a reproducing kernel Hilbert space," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

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