IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i6p2006-2017.html
   My bibliography  Save this article

Semiparametric regression models with additive nonparametric components and high dimensional parametric components

Author

Listed:
  • Du, Pang
  • Cheng, Guang
  • Liang, Hua

Abstract

This paper concerns semiparametric regression models with additive nonparametric components and high dimensional parametric components under sparsity assumptions. To achieve simultaneous model selection for both nonparametric and parametric parts, we introduce a penalty that combines the adaptive empirical L2-norms of the nonparametric component functions and the SCAD penalty on the coefficients in the parametric part. We use the additive partial smoothing spline estimate as the initial estimate and establish its convergence rate with diverging dimensions of parametric components. Our simulation studies reveal excellent model selection performance of the proposed method. An application to an economic study on Canadian household gasoline consumption reveals interesting results.

Suggested Citation

  • Du, Pang & Cheng, Guang & Liang, Hua, 2012. "Semiparametric regression models with additive nonparametric components and high dimensional parametric components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2006-2017.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:2006-2017
    DOI: 10.1016/j.csda.2011.12.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311004282
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.12.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Meinshausen, Nicolai, 2007. "Relaxed Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 374-393, September.
    3. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    4. Radchenko, Peter & James, Gareth M., 2010. "Variable Selection Using Adaptive Nonlinear Interaction Structures in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1541-1553.
    5. Adonis Yatchew & Joungyeo Angela No, 2001. "Household Gasoline Demand in Canada," Econometrica, Econometric Society, vol. 69(6), pages 1697-1709, November.
    6. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    7. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    8. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    9. Ni, Xiao & Zhang, Hao Helen & Zhang, Daowen, 2009. "Automatic model selection for partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2100-2111, October.
    10. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    11. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
    12. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guo, Jie & Tang, Manlai & Tian, Maozai & Zhu, Kai, 2013. "Variable selection in high-dimensional partially linear additive models for composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 56-67.
    2. Manuel Febrero-Bande & Wenceslao González-Manteiga & Manuel Oviedo de la Fuente, 2019. "Variable selection in functional additive regression models," Computational Statistics, Springer, vol. 34(2), pages 469-487, June.
    3. Luo, June & Gerard, Patrick, 2013. "Using thresholding difference-based estimators for variable selection in partial linear models," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2601-2606.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    2. Fabian Scheipl & Thomas Kneib & Ludwig Fahrmeir, 2013. "Penalized likelihood and Bayesian function selection in regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 349-385, October.
    3. Yoshida, Takuma, 2018. "Semiparametric method for model structure discovery in additive regression models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 124-136.
    4. Li, Xinyi & Wang, Li & Nettleton, Dan, 2019. "Sparse model identification and learning for ultra-high-dimensional additive partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 204-228.
    5. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    6. He, Yong & Zhang, Liang & Ji, Jiadong & Zhang, Xinsheng, 2019. "Robust feature screening for elliptical copula regression model," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 568-582.
    7. Zhang, Shucong & Zhou, Yong, 2018. "Variable screening for ultrahigh dimensional heterogeneous data via conditional quantile correlations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 1-13.
    8. Cui, Wenquan & Cheng, Haoyang & Sun, Jiajing, 2018. "An RKHS-based approach to double-penalized regression in high-dimensional partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 201-210.
    9. Xiangyu Wang & Chenlei Leng, 2016. "High dimensional ordinary least squares projection for screening variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 589-611, June.
    10. Lian, Heng & Meng, Jie & Zhao, Kaifeng, 2015. "Spline estimator for simultaneous variable selection and constant coefficient identification in high-dimensional generalized varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 81-103.
    11. Zhenghui Feng & Lu Lin & Ruoqing Zhu & Lixing Zhu, 2020. "Nonparametric variable selection and its application to additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 827-854, June.
    12. Jiang, Liewen & Bondell, Howard D. & Wang, Huixia Judy, 2014. "Interquantile shrinkage and variable selection in quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 208-219.
    13. Min Chen & Yimin Lian & Zhao Chen & Zhengjun Zhang, 2017. "Sure explained variability and independence screening," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 849-883, October.
    14. He, Xin & Mao, Xiaojun & Wang, Zhonglei, 2024. "Nonparametric augmented probability weighting with sparsity," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    15. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    16. Kuang-Yao Lee & Bing Li & Hongyu Zhao, 2016. "Variable selection via additive conditional independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1037-1055, November.
    17. Lian, Heng & Feng, Sanying & Zhao, Kaifeng, 2015. "Parametric and semiparametric reduced-rank regression with flexible sparsity," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 163-174.
    18. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    19. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    20. Guang Cheng & Hao Zhang & Zuofeng Shang, 2015. "Sparse and efficient estimation for partial spline models with increasing dimension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 93-127, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:2006-2017. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.