IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v139y2019icp1-13.html
   My bibliography  Save this article

Estimation for biased partial linear single index models

Author

Listed:
  • Lu, Jun
  • Zhu, Xuehu
  • Lin, Lu
  • Zhu, Lixing

Abstract

In this paper, we propose a novel method to consistently estimate, at the root-n rate, the coefficient parameters in a biased partial linear single-index model whose error term does not have zero conditional expectation. To achieve this purpose, we first transfer the model to a pro forma linear model and then introduce an artificial variable into a linear bias correction model. Based on the bias correction model, the parameters can then be consistently estimated by the linear least squares method. Both numerical studies and real data analyses are conducted to show the effectiveness of the proposed estimation procedure.

Suggested Citation

  • Lu, Jun & Zhu, Xuehu & Lin, Lu & Zhu, Lixing, 2019. "Estimation for biased partial linear single index models," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 1-13.
  • Handle: RePEc:eee:csdana:v:139:y:2019:i:c:p:1-13
    DOI: 10.1016/j.csda.2019.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319300738
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2019.03.006?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. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    2. Lin, Lu & Zhu, Lixing & Gai, Yujie, 2016. "Inference for biased models: A quasi-instrumental variable approach," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 22-36.
    3. Zhu, Xuehu & Wang, Tao & Zhao, Junlong & Zhu, Lixing, 2017. "Inference for biased transformation models," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 105-120.
    4. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    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. Junmin Liu & Deli Zhu & Luoyao Yu & Xuehu Zhu, 2023. "Specification testing of partially linear single-index models: a groupwise dimension reduction-based adaptive-to-model approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 232-262, March.
    2. Xuehu Zhu & Jun Lu & Jun Zhang & Lixing Zhu, 2021. "Testing for conditional independence: A groupwise dimension reduction‐based adaptive‐to‐model approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 549-576, June.

    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. Lai, Peng & Wang, Qihua & Lian, Heng, 2012. "Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 422-432.
    2. repec:wyi:journl:002176 is not listed on IDEAS
    3. Huang, Zhensheng & Pang, Zhen, 2012. "Corrected empirical likelihood inference for right-censored partially linear single-index model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 276-284.
    4. Xu, Mengshan & Otsu, Taisuke, 2020. "Score estimation of monotone partially linear index model," LSE Research Online Documents on Economics 106698, London School of Economics and Political Science, LSE Library.
    5. Lai, Peng & Wang, Qihua & Zhou, Xiao-Hua, 2014. "Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 241-256.
    6. Taisuke Otsu & Mengshan Xu, 2019. "Score estimation of monotone partially linear index model," STICERD - Econometrics Paper Series 603, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Qingming Zou & Zhongyi Zhu, 2014. "M-estimators for single-index model using B-spline," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 225-246, February.
    8. Minggen Lu, 2018. "Spline-based quasi-likelihood estimation of mixed Poisson regression with single-index models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 1-17, January.
    9. Wu, Jingwei & Peng, Hanxiang & Tu, Wanzhu, 2019. "Large-sample estimation and inference in multivariate single-index models," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 382-396.
    10. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    11. Huang, Zhensheng & Zhang, Riquan, 2011. "Efficient empirical-likelihood-based inferences for the single-index model," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 937-947, May.
    12. Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Quadratic inference functions for partially linear single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 115-127.
    13. Gueuning, Thomas & Claeskens, Gerda, 2016. "Confidence intervals for high-dimensional partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 13-29.
    14. Jianglin Fang & Wanrong Liu & Xuewen Lu, 2018. "Empirical likelihood for heteroscedastic partially linear single-index models with growing dimensional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 255-281, April.
    15. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    16. Zhiyong Chen & Jianbao Chen, 2022. "Bayesian analysis of partially linear, single-index, spatial autoregressive models," Computational Statistics, Springer, vol. 37(1), pages 327-353, March.
    17. Feng, Sanying & Xue, Liugen, 2015. "Model detection and estimation for single-index varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 227-244.
    18. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    19. Stéphane GREGOIR & Tristan-Pierre MAURY, 2014. "Empowerment Zones And The Housing Market In Paris Inner City," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 40, pages 69-82.
    20. Suli Cheng & Jianbao Chen, 2021. "Estimation of partially linear single-index spatial autoregressive model," Statistical Papers, Springer, vol. 62(1), pages 495-531, February.
    21. Huang, Lei & Jiang, Hui & Wang, Huixia, 2019. "A novel partial-linear single-index model for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 110-122.

    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:139:y:2019:i:c:p:1-13. 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.