IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/106698.html
   My bibliography  Save this paper

Score estimation of monotone partially linear index model

Author

Listed:
  • Xu, Mengshan
  • Otsu, Taisuke

Abstract

This paper studies semiparametric estimation of a partially linear single index model with a monotone link function. Our estimator is an extension of the score-type estimator developed by Balabdaoui et al. (2019) for the monotone single index model, which profiles out the unknown link function by isotonic regression. An attractive feature of the proposed estimator is that it is free from tuning parameters for nonparametric smoothing. We show that our estimator for the finite-dimensional components is √n- consistent and asymptotically normal. By introducing an additional smoothing to obtain the efficient score, we propose an asymptotically efficient estimator for the finite-dimensional components. Furthermore, we establish the asymptotic validity of a bootstrap inference method based the score-type estimator, which is also free from tuning parameters. A simulation study illustrates the usefulness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:106698
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/106698/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    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. Groeneboom,Piet & Jongbloed,Geurt, 2014. "Nonparametric Estimation under Shape Constraints," Cambridge Books, Cambridge University Press, number 9780521864015, January.
    3. Yanyuan Ma & Liping Zhu, 2013. "Doubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 305-322, March.
    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.
    5. Fadoua Balabdaoui & Piet Groeneboom & Kim Hendrickx, 2019. "Score estimation in the monotone single‐index model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 517-544, June.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. 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.
    4. Jia Chen & Degui Li & Hua Liang & Suojin Wang, 2014. "Semiparametric GEE Analysis in Partially Linear Single-Index Models for Longitudinal Data," Discussion Papers 14/26, Department of Economics, University of York.
    5. Lai, Peng & Wang, Qihua, 2014. "Semiparametric efficient estimation for partially linear single-index models with responses missing at random," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 33-50.
    6. Yoici Arai & Taisuke Otsu & Mengshan Xu, 2022. "GLS under monotone heteroskedasticity," STICERD - Econometrics Paper Series 625, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. 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.
    8. repec:wyi:journl:002176 is not listed on IDEAS
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    21. 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.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ehl:lserod:106698. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.