IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v97y2013i4p317-347.html
   My bibliography  Save this article

Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables

Author

Listed:
  • Xiaofeng Lv
  • Rui Li

Abstract

In this paper, we consider the estimation and inference of the parameters and the nonparametric part in partially linear quantile regression models with responses that are missing at random. First, we extend the normal approximation (NA)-based methods of Sun ( 2005 ) to the missing data case. However, the asymptotic covariance matrices of NA-based methods are difficult to estimate, which complicates inference. To overcome this problem, alternatively, we propose the smoothed empirical likelihood (SEL)-based methods. We define SEL statistics for the parameters and the nonparametric part and demonstrate that the limiting distributions of the statistics are Chi-squared distributions. Accordingly, confidence regions can be obtained without the estimation of the asymptotic covariance matrices. Monte Carlo simulations are conducted to evaluate the performance of the proposed method. Finally, the NA- and SEL-based methods are applied to real data. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Xiaofeng Lv & Rui Li, 2013. "Smoothed empirical likelihood analysis of partially linear quantile regression models with missing response variables," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 317-347, October.
    • Handle: RePEc:spr:alstar:v:97:y:2013:i:4:p:317-347
    DOI: 10.1007/s10182-013-0210-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10182-013-0210-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10182-013-0210-4?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. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    2. Chaudhuri, Probal, 1991. "Global nonparametric estimation of conditional quantile functions and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 246-269, November.
    3. Qin, Gengsheng & Tsao, Min, 2003. "Empirical likelihood inference for median regression models for censored survival data," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 416-430, May.
    4. Blundell, Richard & Powell, James L., 2007. "Censored regression quantiles with endogenous regressors," Journal of Econometrics, Elsevier, vol. 141(1), pages 65-83, November.
    5. Lee, Sokbae, 2007. "Endogeneity in quantile regression models: A control function approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 1131-1158, December.
    6. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(2), pages 173-205, April.
    7. Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.
    8. Xingdong Feng & Xuming He & Jianhua Hu, 2011. "Wild bootstrap for quantile regression," Biometrika, Biometrika Trust, vol. 98(4), pages 995-999.
    9. Chen, Songnian & Khan, Shakeeb, 2001. "Semiparametric Estimation Of A Partially Linear Censored Regression Model," Econometric Theory, Cambridge University Press, vol. 17(3), pages 567-590, June.
    10. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    11. Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
    12. Lee, Sokbae, 2003. "Efficient Semiparametric Estimation Of A Partially Linear Quantile Regression Model," Econometric Theory, Cambridge University Press, vol. 19(1), pages 1-31, February.
    13. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    14. Liang, Hua, 2008. "Generalized partially linear models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 880-895, May.
    15. Zhou, Yong & Wan, Alan T. K & Wang, Xiaojing, 2008. "Estimating Equations Inference With Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1187-1199.
    16. Song, Song & Ritov, Ya’acov & Härdle, Wolfgang K., 2012. "Bootstrap confidence bands and partial linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 244-262.
    17. Yiguo Sun, 2005. "Semiparametric Efficient Estimation of Partially Linear Quantile Regression Models," Annals of Economics and Finance, Society for AEF, vol. 6(1), pages 105-127, May.
    18. Hua Liang & Suojin Wang & Raymond J. Carroll, 2007. "Partially linear models with missing response variables and error-prone covariates," Biometrika, Biometrika Trust, vol. 94(1), pages 185-198.
    19. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    20. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(1), pages 105-121, February.
    21. Horowitz, Joel L., 2002. "Bootstrap critical values for tests based on the smoothed maximum score estimator," Journal of Econometrics, Elsevier, vol. 111(2), pages 141-167, December.
    22. Yongsong Qin & Jianjun Li, 2011. "Empirical likelihood for partially linear models with missing responses at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 497-511.
    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. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 195-216, June.
    2. Bindele, Huybrechts F., 2018. "Covariates missing at random under signed-rank inference," Econometrics and Statistics, Elsevier, vol. 8(C), pages 78-93.
    3. Peixin Zhao & Xinrong Tang, 2016. "Imputation based statistical inference for partially linear quantile regression models with missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 991-1009, November.
    4. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2019. "Weighted quantile regression for censored data with application to export duration data," Statistical Papers, Springer, vol. 60(4), pages 1161-1192, August.
    5. Chang-Sheng Liu & Han-Ying Liang, 2023. "Bayesian empirical likelihood of quantile regression with missing observations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 285-313, April.
    6. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2017. "Bootstrap-calibrated empirical likelihood confidence intervals for the difference between two Gini indexes," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(2), pages 195-216, June.
    7. 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.
    8. 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. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    2. Guo, Jing & Wang, Lei & Zhang, Zhengyu, 2022. "Identification and estimation of a heteroskedastic censored regression model with random coefficient dummy endogenous regressors," Economic Modelling, Elsevier, vol. 110(C).
    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. Kaplan, David M. & Sun, Yixiao, 2017. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," Econometric Theory, Cambridge University Press, vol. 33(1), pages 105-157, February.
    5. Wu, Chaojiang & Yu, Yan, 2014. "Partially linear modeling of conditional quantiles using penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 170-187.
    6. Joel L. Horowitz, 2018. "Bootstrap Methods in Econometrics," Papers 1809.04016, arXiv.org.
    7. Joel L. Horowitz, 2018. "Bootstrap methods in econometrics," CeMMAP working papers CWP53/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    9. Jerome M. Krief, 2011. "Kernel Weighted Smoothed Maximum Score Estimation for Applied Work," Departmental Working Papers 2011-07, Department of Economics, Louisiana State University.
    10. 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.
    11. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    12. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    13. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    14. Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(4), pages 614-632, August.
    15. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
    16. Xiaofeng Lv & Gupeng Zhang & Xinkuo Xu & Qinghai Li, 2019. "Weighted quantile regression for censored data with application to export duration data," Statistical Papers, Springer, vol. 60(4), pages 1161-1192, August.
    17. He, Xuming & Pan, Xiaoou & Tan, Kean Ming & Zhou, Wen-Xin, 2023. "Smoothed quantile regression with large-scale inference," Journal of Econometrics, Elsevier, vol. 232(2), pages 367-388.
    18. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    19. repec:hal:journl:peer-00732534 is not listed on IDEAS
    20. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series 1109, University of St. Gallen, School of Economics and Political Science.
    21. Peixin Zhao & Xinrong Tang, 2016. "Imputation based statistical inference for partially linear quantile regression models with missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 991-1009, November.

    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:97:y:2013:i:4:p:317-347. 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.