IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v144y2020ics0167947319302221.html
   My bibliography  Save this article

Single-index modal regression via outer product gradients

Author

Listed:
  • Yang, Jing
  • Tian, Guoliang
  • Lu, Fang
  • Lu, Xuewen

Abstract

Most existing methods for single-index models (SIM) were focused on either mean regression or quantile regression, while the former is sensitive to outliers or heavy tailed distributions and the latter may lose efficiency for normally distributed data. Then a robust, efficient and easily implemented estimation procedure for index coefficient in SIM is developed by integrating the ideas of local modal regression and outer product gradients. Under some mild conditions, we establish the asymptotic normality of the proposed estimators. We further discuss the optimal choices of tuning parameters including one common bandwidth for nonparametric polynomial smoothing and another key bandwidth that controls the robustness and efficiency of the estimator, based on the derived theories. A practical modified EM algorithm is also presented for implementation. Finally, some simulation studies and two real data analysis are conducted to confirm the merits and theoretical findings of the novel method.

Suggested Citation

  • Yang, Jing & Tian, Guoliang & Lu, Fang & Lu, Xuewen, 2020. "Single-index modal regression via outer product gradients," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302221
    DOI: 10.1016/j.csda.2019.106867
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319302221
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.106867?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. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    2. 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.
    3. Jiang, Rong & Qian, Wei-Min & Zhou, Zhan-Gong, 2016. "Weighted composite quantile regression for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 34-48.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    6. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    7. Kong, Efang & Xia, Yingcun, 2012. "A Single-Index Quantile Regression Model And Its Estimation," Econometric Theory, Cambridge University Press, vol. 28(4), pages 730-768, August.
    8. Liu, Jicai & Zhang, Riquan & Zhao, Weihua & Lv, Yazhao, 2013. "A robust and efficient estimation method for single index models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 226-238.
    9. Wang, Qin & Yin, Xiangrong, 2008. "A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4512-4520, May.
    10. Weixin Yao & Bruce Lindsay & Runze Li, 2012. "Local modal regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 647-663.
    11. Weihua Zhao & Riquan Zhang & Jicai Liu & Yazhao Lv, 2014. "Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 165-191, February.
    12. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1112-1137, December.
    13. Riquan Zhang & Weihua Zhao & Jicai Liu, 2013. "Robust estimation and variable selection for semiparametric partially linear varying coefficient model based on modal regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 523-544, June.
    14. Weixin Yao & Longhai Li, 2014. "A New Regression Model: Modal Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 656-671, September.
    15. Li, Jianbo & Lian, Heng & Jiang, Xuejun & Song, Xinyuan, 2018. "Estimation and testing for time-varying quantile single-index models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 118(C), pages 66-83.
    16. Yang, Hu & Yang, Jing, 2014. "A robust and efficient estimation and variable selection method for partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 227-242.
    17. Jiang, Xuejun & Li, Jingzhi & Xia, Tian & Yan, Wanfeng, 2016. "Robust and efficient estimation with weighted composite quantile regression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 413-423.
    18. Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 180-191.
    19. Yang, Hu & Guo, Chaohui & Lv, Jing, 2014. "A robust and efficient estimation method for single-index varying-coefficient models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 119-127.
    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. Han, Jinyue & Wang, Jun & Gao, Wei & Tang, Man-Lai, 2023. "Estimation of the directions for unknown parameters in semiparametric models," MPRA Paper 116365, University Library of Munich, Germany.

    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. Yang, Hu & Yang, Jing, 2014. "A robust and efficient estimation and variable selection method for partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 227-242.
    2. 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.
    3. Wang, Kangning & Li, Shaomin, 2021. "Robust distributed modal regression for massive data," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    4. Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 180-191.
    5. Huybrechts F. Bindele & Ash Abebe & Karlene N. Meyer, 2018. "General rank-based estimation for regression single index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1115-1146, October.
    6. Ash Abebe & Huybrechts F. Bindele & Masego Otlaadisa & Boikanyo Makubate, 2021. "Robust estimation of single index models with responses missing at random," Statistical Papers, Springer, vol. 62(5), pages 2195-2225, October.
    7. Bousebata, Meryem & Enjolras, Geoffroy & Girard, Stéphane, 2023. "Extreme partial least-squares," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    8. Wang, Kangning & Li, Shaomin & Sun, Xiaofei & Lin, Lu, 2019. "Modal regression statistical inference for longitudinal data semivarying coefficient models: Generalized estimating equations, empirical likelihood and variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 257-276.
    9. Jiang, Rong & Qian, Wei-Min & Zhou, Zhan-Gong, 2016. "Weighted composite quantile regression for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 34-48.
    10. Han, Zhong-Cheng & Lin, Jin-Guan & Zhao, Yan-Yong, 2020. "Adaptive semiparametric estimation for single index models with jumps," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    11. Bucher, Axel & El Ghouch, Anouar & Van Keilegom, Ingrid, 2014. "Single-index quantile regression models for censored data," LIDAM Discussion Papers ISBA 2014001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Jing Sun, 2016. "Composite quantile regression for single-index models with asymmetric errors," Computational Statistics, Springer, vol. 31(1), pages 329-351, March.
    13. Liu, Jicai & Zhang, Riquan & Zhao, Weihua & Lv, Yazhao, 2013. "A robust and efficient estimation method for single index models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 226-238.
    14. Yang, Jing & Yang, Hu, 2016. "A robust penalized estimation for identification in semiparametric additive models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 268-277.
    15. Qingyang Liu & Xianzheng Huang & Haiming Zhou, 2024. "The Flexible Gumbel Distribution: A New Model for Inference about the Mode," Stats, MDPI, vol. 7(1), pages 1-16, March.
    16. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    17. Lv, Zhike & Zhu, Huiming & Yu, Keming, 2014. "Robust variable selection for nonlinear models with diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 90-97.
    18. Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    19. 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.
    20. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2015. "Quantile regression and variable selection of partial linear single-index model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 375-409, April.

    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:144:y:2020:i:c:s0167947319302221. 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.