IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v62y2021i3d10.1007_s00362-019-01135-6.html
   My bibliography  Save this article

Goodness-of-fit tests for quantile regression with missing responses

Author

Listed:
  • Ana Pérez-González

    (University of Vigo)

  • Tomás R. Cotos-Yáñez

    (University of Vigo)

  • Wenceslao González-Manteiga

    (Universidade de Santiago de Compostela)

  • Rosa M. Crujeiras-Casais

    (Universidade de Santiago de Compostela)

Abstract

Goodness-of-fit tests for quantile regression models, in the presence of missing observations in the response variable, are introduced and analysed in this paper. The different proposals are based on the construction of empirical processes considering three different approaches which involve the use of the gradient vector of the quantile function, a linear projection of the covariates (suitable for high-dimensional settings) and a projection of the estimating equations. Besides, two types of estimators for the null parametric model to be tested are considered. The performance of the different test statistics is analysed in an extensive simulation study. An application to real data is also included.

Suggested Citation

  • Ana Pérez-González & Tomás R. Cotos-Yáñez & Wenceslao González-Manteiga & Rosa M. Crujeiras-Casais, 2021. "Goodness-of-fit tests for quantile regression with missing responses," Statistical Papers, Springer, vol. 62(3), pages 1231-1264, June.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01135-6
    DOI: 10.1007/s00362-019-01135-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-019-01135-6
    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/s00362-019-01135-6?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. 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.
    2. Chen Dong & Guodong Li & Xingdong Feng, 2019. "Lack‐of‐fit tests for quantile regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 629-648, July.
    3. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    4. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
    5. Sun, Zhihua & Wang, Qihua & Dai, Pengjie, 2009. "Model checking for partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 636-651, April.
    6. Hong-Xia Xu & Guo-Liang Fan & Han-Ying Liang, 2017. "Hypothesis test on response mean with inequality constraints under data missing when covariables are present," Statistical Papers, Springer, vol. 58(1), pages 53-75, March.
    7. Zheng, John Xu, 1998. "A Consistent Nonparametric Test Of Parametric Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 123-138, February.
    8. Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1030-1051, December.
    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. Wangli Xu & Xu Guo, 2013. "Nonparametric checks for varying coefficient models with missing response at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 459-482, May.
    11. Herman J. Bierens & Donna K. Ginther, 2001. "Integrated Conditional Moment testing of quantile regression models," Empirical Economics, Springer, vol. 26(1), pages 307-324.
    12. Xingdong Feng & Xuming He & Jianhua Hu, 2011. "Wild bootstrap for quantile regression," Biometrika, Biometrika Trust, vol. 98(4), pages 995-999.
    13. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
    14. He X. & Zhu L-X., 2003. "A Lack-of-Fit Test for Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1013-1022, January.
    15. Sun, Zhihua & Chen, Feifei & Zhou, Xiaohua & Zhang, Qingzhao, 2017. "Improved model checking methods for parametric models with responses missing at random," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 147-161.
    16. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    17. 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.
    18. 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.
    19. Wangli Xu & Lixing Zhu, 2013. "Testing the adequacy of varying coefficient models with missing responses at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 53-69, January.
    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. 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.
    2. Tu, Yundong & Liang, Han-Ying & Wang, Qiying, 2022. "Nonparametric inference for quantile cointegrations with stationary covariates," Journal of Econometrics, Elsevier, vol. 230(2), pages 453-482.
    3. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
    4. 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.
    5. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
    6. Feng, Xingdong & Liu, Qiaochu & Wang, Caixing, 2023. "A lack-of-fit test for quantile regression process models," Statistics & Probability Letters, Elsevier, vol. 192(C).
    7. Antonio Galvao & Kengo Kato & Gabriel Montes-Rojas & Jose Olmo, 2014. "Testing linearity against threshold effects: uniform inference in quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 413-439, April.
    8. Komunjer, Ivana, 2013. "Quantile Prediction," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 961-994, Elsevier.
    9. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.
    10. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
    11. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
    12. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2021. "A Nonparametric Test for Testing Heterogeneity in Conditional Quantile Treatment Effects," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202117, University of Kansas, Department of Economics, revised Aug 2021.
    13. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    14. Xu, Hong-Xia & Fan, Guo-Liang & Chen, Zhen-Long, 2017. "Hypothesis tests in partial linear errors-in-variables models with missing response," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 219-229.
    15. Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(4), pages 614-632, August.
    16. repec:hal:journl:peer-00732534 is not listed on IDEAS
    17. Kostov, Philip & Patton, Myles & Moss, Joan E. & McErlean, Seamus, 2005. "Does Gibrat's Law Hold Amongst Dairy Farmers in Northern Ireland?," 2005 International Congress, August 23-27, 2005, Copenhagen, Denmark 24775, European Association of Agricultural Economists.
    18. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    19. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    20. Francesco Bravo, 2013. "Partially linear varying coefficient models with missing at random responses," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 721-762, August.
    21. Liu, Jicai & Si, Yuefeng & Niu, Yong & Zhang, Riquan, 2022. "Projection quantile correlation and its use in high-dimensional grouped variable screening," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).

    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:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01135-6. 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.