IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v29y2013i06p1136-1161_00.html
   My bibliography  Save this article

Generalized Additive Partial Linear Models With High-Dimensional Covariates

Author

Listed:
  • Lian, Heng
  • Liang, Hua

Abstract

This paper studies generalized additive partial linear models with high-dimensional covariates. We are interested in which components (including parametric and nonparametric components) are nonzero. The additive nonparametric functions are approximated by polynomial splines. We propose a doubly penalized procedure to obtain an initial estimate and then use the adaptive least absolute shrinkage and selection operator to identify nonzero components and to obtain the final selection and estimation results. We establish selection and estimation consistency of the estimator in addition to asymptotic normality for the estimator of the parametric components by employing a penalized quasi-likelihood. Thus our estimator is shown to have an asymptotic oracle property. Monte Carlo simulations show that the proposed procedure works well with moderate sample sizes.

Suggested Citation

  • Lian, Heng & Liang, Hua, 2013. "Generalized Additive Partial Linear Models With High-Dimensional Covariates," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1136-1161, December.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:06:p:1136-1161_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466613000029/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Wu, Cen & Zhang, Qingzhao & Jiang, Yu & Ma, Shuangge, 2018. "Robust network-based analysis of the associations between (epi)genetic measurements," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 119-130.
    2. 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.
    3. Lin, Hongmei & Lian, Heng & Liang, Hua, 2019. "Rank reduction for high-dimensional generalized additive models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 672-684.
    4. Heng Lian, 2020. "Asymptotics of the Non‐parametric Function for B‐splines‐based Estimation in Partially Linear Models," International Statistical Review, International Statistical Institute, vol. 88(1), pages 142-154, April.

    More about this item

    Statistics

    Access and download statistics

    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:cup:etheor:v:29:y:2013:i:06:p:1136-1161_00. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    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.