IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v180y2020ics0047259x20302505.html
   My bibliography  Save this article

Single-index composite quantile regression for massive data

Author

Listed:
  • Jiang, Rong
  • Yu, Keming

Abstract

Composite quantile regression (CQR) is becoming increasingly popular due to its robustness from quantile regression. Recently, the CQR method has been studied extensively with single-index models. However, the numerical inference of CQR methods for single-index models must involve iteration. In this study, we propose a non-iterative CQR (NICQR) estimation algorithm and derive the asymptotic distribution of the proposed estimator. Moreover, we extend the NICQR method to the analysis of massive datasets via a divide-and-conquer strategy. The proposed approach significantly reduces the computing time and the required primary memory. Simulation studies and two real data applications are conducted to illustrate the finite sample performance of the proposed methods.

Suggested Citation

  • Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:jmvana:v:180:y:2020:i:c:s0047259x20302505
    DOI: 10.1016/j.jmva.2020.104669
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X20302505
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2020.104669?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. 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.
    2. Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2016. "Single-index composite quantile regression with heteroscedasticity and general error distributions," Statistical Papers, Springer, vol. 57(1), pages 185-203, March.
    3. Dungang Liu & Regina Y. Liu & Minge Xie, 2015. "Multivariate Meta-Analysis of Heterogeneous Studies Using Only Summary Statistics: Efficiency and Robustness," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 326-340, March.
    4. 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.
    5. Tian, Yuzhu & Zhu, Qianqian & Tian, Maozai, 2016. "Estimation of linear composite quantile regression using EM algorithm," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 183-191.
    6. Runze Li & Dennis K.J. Lin & Bing Li, 2013. "Statistical inference in massive data sets," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(5), pages 399-409, September.
    7. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    8. 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.
    9. Yanlin Tang & Huixia Judy Wang & Hua Liang, 2018. "Composite Estimation for Single‐Index Models with Responses Subject to Detection Limits," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 444-464, September.
    10. D. Y. Lin & D. Zeng, 2010. "On the relative efficiency of using summary statistics versus individual-level data in meta-analysis," Biometrika, Biometrika Trust, vol. 97(2), pages 321-332.
    11. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    12. 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.
    13. Xie, Minge & Singh, Kesar & Strawderman, William E., 2011. "Confidence Distributions and a Unifying Framework for Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 320-333.
    14. Rémillard, Bruno & Nasri, Bouchra & Bouezmarni, Taoufik, 2017. "On copula-based conditional quantile estimators," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 14-20.
    15. Christou, Eliana & Akritas, Michael G., 2016. "Single index quantile regression for heteroscedastic data," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 169-182.
    16. Wei Lin & K. B. Kulasekera, 2007. "Identifiability of single-index models and additive-index models," Biometrika, Biometrika Trust, vol. 94(2), pages 496-501.
    17. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    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. Yunquan Song & Zitong Li & Minglu Fang, 2022. "Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    2. Rong Jiang & Mengxian Sun, 2022. "Single-index composite quantile regression for ultra-high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 443-460, 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. Rong Jiang & Mengxian Sun, 2022. "Single-index composite quantile regression for ultra-high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 443-460, June.
    2. 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.
    3. Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2016. "Single-index composite quantile regression with heteroscedasticity and general error distributions," Statistical Papers, Springer, vol. 57(1), pages 185-203, March.
    4. 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).
    5. 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.
    6. Jing Sun, 2016. "Composite quantile regression for single-index models with asymmetric errors," Computational Statistics, Springer, vol. 31(1), pages 329-351, March.
    7. Zhang, Wenyang & Li, Degui & Xia, Yingcun, 2015. "Estimation in generalised varying-coefficient models with unspecified link functions," Journal of Econometrics, Elsevier, vol. 187(1), pages 238-255.
    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. Yunquan Song & Zitong Li & Minglu Fang, 2022. "Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    10. Fengrui Di & Lei Wang, 2022. "Multi-round smoothed composite quantile regression for distributed data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 869-893, October.
    11. 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.
    12. Rong Jiang & Wei-wei Chen & Xin Liu, 2021. "Adaptive quantile regressions for massive datasets," Statistical Papers, Springer, vol. 62(4), pages 1981-1995, August.
    13. 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.
    14. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2014. "Quantile regression and variable selection for the single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1565-1577, July.
    15. 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.
    16. Zijuan Chen & Suojin Wang, 2023. "Inferences for extended partially linear single-index models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 602-622, June.
    17. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.
    18. Tang, Lu & Zhou, Ling & Song, Peter X.-K., 2020. "Distributed simultaneous inference in generalized linear models via confidence distribution," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    19. Claudio Agostinelli & Ana M. Bianco & Graciela Boente, 2020. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 855-893, June.
    20. Huilan Liu & Hu Yang & Changgen Peng, 2019. "Weighted composite quantile regression for single index model with missing covariates at random," Computational Statistics, Springer, vol. 34(4), pages 1711-1740, December.

    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:jmvana:v:180:y:2020:i:c:s0047259x20302505. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.