IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v101y2017i1d10.1007_s10182-016-0278-8.html
   My bibliography  Save this article

Smoothed empirical likelihood for quantile regression models with response data missing at random

Author

Listed:
  • Shuanghua Luo

    (Xi’an Jiaotong University
    Xi’an Polytechnic University)

  • Changlin Mei

    (Xi’an Jiaotong University)

  • Cheng-yi Zhang

    (Xi’an Polytechnic University)

Abstract

This paper studies smoothed quantile linear regression models with response data missing at random. Three smoothed quantile empirical likelihood ratios are proposed first and shown to be asymptotically Chi-squared. Then, the confidence intervals for the regression coefficients are constructed without the estimation of the asymptotic covariance. Furthermore, a class of estimators for the regression parameter is presented to derive its asymptotic distribution. Simulation studies are conducted to assess the finite sample performance. Finally, a real-world data set is analyzed to illustrated the effectiveness of the proposed methods.

Suggested Citation

  • Shuanghua Luo & Changlin Mei & Cheng-yi Zhang, 2017. "Smoothed empirical likelihood for quantile regression models with response data missing at random," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 95-116, January.
    • Handle: RePEc:spr:alstar:v:101:y:2017:i:1:d:10.1007_s10182-016-0278-8
    DOI: 10.1007/s10182-016-0278-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-016-0278-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10182-016-0278-8?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. Wang, Qihua & Sun, Zhihua, 2007. "Estimation in partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1470-1493, August.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    3. Ying Wei & Yanyuan Ma & Raymond J. Carroll, 2012. "Multiple imputation in quantile regression," Biometrika, Biometrika Trust, vol. 99(2), pages 423-438.
    4. Yichuan Zhao & Song Yang, 2008. "Empirical likelihood inference for censored median regression with weighted empirical hazard functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 441-457, June.
    5. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    6. Liugen Xue, 2009. "Empirical Likelihood Confidence Intervals for Response Mean with Data Missing at Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 671-685, December.
    7. Cheng Yong Tang & Yongsong Qin, 2012. "An efficient empirical likelihood approach for estimating equations with missing data," Biometrika, Biometrika Trust, vol. 99(4), pages 1001-1007.
    8. Stuart R. Lipsitz & Lue Ping Zhao & Geert Molenberghs, 1998. "A semiparametric method of multiple imputation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 127-144.
    9. Xuerong Chen & Alan T. K. Wan & Yong Zhou, 2015. "Efficient Quantile Regression Analysis With Missing Observations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 723-741, June.
    10. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(2), pages 173-205, April.
    11. Marc Aerts, 2002. "Local multiple imputation," Biometrika, Biometrika Trust, vol. 89(2), pages 375-388, June.
    12. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    13. Xue, Liugen, 2009. "Empirical likelihood for linear models with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1353-1366, August.
    14. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
    15. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    16. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    17. Wang, You-Gan & Shao, Quanxi & Zhu, Min, 2009. "Quantile regression without the curse of unsmoothness," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3696-3705, August.
    18. Zhao, Yichuan & Chen, Feiming, 2008. "Empirical likelihood inference for censored median regression model via nonparametric kernel estimation," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 215-231, February.
    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. Hong-Xia Xu & Guo-Liang Fan & Zhen-Long Chen & Jiang-Feng Wang, 2018. "Weighted quantile regression and testing for varying-coefficient models with randomly truncated data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 565-588, October.
    2. Xiaohui Yuan & Huixian Li & Tianqing Liu, 2021. "Empirical likelihood inference for rank regression with doubly truncated data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 25-73, March.
    3. Xiaoshuang Zhou & Peixin Zhao & Yujie Gai, 2022. "Imputation-based empirical likelihood inferences for partially nonlinear quantile regression models with missing responses," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 705-722, December.

    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. Yu Shen & Han-Ying Liang, 2018. "Quantile regression and its empirical likelihood with missing response at random," Statistical Papers, Springer, vol. 59(2), pages 685-707, June.
    2. Xuerong Chen & Alan T. K. Wan & Yong Zhou, 2015. "Efficient Quantile Regression Analysis With Missing Observations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 723-741, June.
    3. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    4. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    5. Tang, Cheng Yong & Leng, Chenlei, 2012. "An empirical likelihood approach to quantile regression with auxiliary information," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 29-36.
    6. Lin, Wei & Cai, Zongwu & Li, Zheng & Su, Li, 2015. "Optimal smoothing in nonparametric conditional quantile derivative function estimation," Journal of Econometrics, Elsevier, vol. 188(2), pages 502-513.
    7. Bindele, Huybrechts F., 2018. "Covariates missing at random under signed-rank inference," Econometrics and Statistics, Elsevier, vol. 8(C), pages 78-93.
    8. Marcelo Fernandes & Emmanuel Guerre & Eduardo Horta, 2021. "Smoothing Quantile Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 338-357, January.
    9. Sherwood, Ben, 2016. "Variable selection for additive partial linear quantile regression with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 206-223.
    10. Cheng, Hao, 2021. "Importance sampling imputation algorithms in quantile regression with their application in CGSS data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 498-508.
    11. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    12. Aiai Yu & Yujie Zhong & Xingdong Feng & Ying Wei, 2023. "Quantile regression for nonignorable missing data with its application of analyzing electronic medical records," Biometrics, The International Biometric Society, vol. 79(3), pages 2036-2049, September.
    13. Xue, Liugen & Xue, Dong, 2011. "Empirical likelihood for semiparametric regression model with missing response data," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 723-740, April.
    14. Conde-Amboage, Mercedes & Sánchez-Sellero, César & González-Manteiga, Wenceslao, 2015. "A lack-of-fit test for quantile regression models with high-dimensional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 128-138.
    15. Philip Kostov, 2013. "Empirical likelihood estimation of the spatial quantile regression," Journal of Geographical Systems, Springer, vol. 15(1), pages 51-69, January.
    16. Su, Liangjun & Hoshino, Tadao, 2016. "Sieve instrumental variable quantile regression estimation of functional coefficient models," Journal of Econometrics, Elsevier, vol. 191(1), pages 231-254.
    17. Ke, Baofang & Zhao, Weihua & Wang, Lei, 2023. "Smoothed tensor quantile regression estimation for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    18. Cai, Zongwu & Chen, Linna & Fang, Ying, 2018. "A semiparametric quantile panel data model with an application to estimating the growth effect of FDI," Journal of Econometrics, Elsevier, vol. 206(2), pages 531-553.
    19. Hu, Yanan & Yang, Yaqi & Wang, Chunyu & Tian, Maozai, 2017. "Imputation in nonparametric quantile regression with complex data," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 120-130.
    20. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.

    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:spr:alstar:v:101:y:2017:i:1:d:10.1007_s10182-016-0278-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.