IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v28y2019i1d10.1007_s11749-018-0591-5.html
   My bibliography  Save this article

Plug-in marginal estimation under a general regression model with missing responses and covariates

Author

Listed:
  • Ana M. Bianco

    (Universidad de Buenos Aires and CONICET Ciudad Universitaria)

  • Graciela Boente

    (Universidad de Buenos Aires and IMAS, CONICET Ciudad Universitaria)

  • Wenceslao González-Manteiga

    (Universidad de Santiago de Compostela)

  • Ana Pérez-González

    (Universidad de Vigo)

Abstract

In this paper, we consider a general regression model where missing data occur in the response and in the covariates. Our aim is to estimate the marginal distribution function and a marginal functional, such as the mean, the median or any $$\alpha $$ α -quantile of the response variable. A missing at random condition is assumed in order to prevent from bias in the estimation of the marginal measures under a non-ignorable missing mechanism. We give two different approaches for the estimation of the responses distribution function and of a given marginal functional, involving inverse probability weighting and the convolution of the distribution function of the observed residuals and that of the observed estimated regression function. Through a Monte Carlo study and two real data sets, we illustrate the behaviour of our proposals.

Suggested Citation

  • Ana M. Bianco & Graciela Boente & Wenceslao González-Manteiga & Ana Pérez-González, 2019. "Plug-in marginal estimation under a general regression model with missing responses and covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 106-146, March.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:1:d:10.1007_s11749-018-0591-5
    DOI: 10.1007/s11749-018-0591-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-018-0591-5
    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/s11749-018-0591-5?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. Bianco, Ana & Boente, Graciela & González-Manteiga, Wenceslao & Pérez-González, Ana, 2010. "Estimation of the marginal location under a partially linear model with missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 546-564, February.
    2. Song Chen & Ingrid Van Keilegom, 2013. "Estimation in semiparametric models with missing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 785-805, August.
    3. Liang H. & Wang S. & Robins J.M. & Carroll R.J., 2004. "Estimation in Partially Linear Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 357-367, January.
    4. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    5. 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.
    6. Marc Aerts, 2002. "Local multiple imputation," Biometrika, Biometrika Trust, vol. 89(2), pages 375-388, June.
    7. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    8. Bravo, Francesco, 2015. "Semiparametric estimation with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 329-346.
    9. 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.
    10. Chen, Qingxia & Ibrahim, Joseph G. & Chen, Ming-Hui & Senchaudhuri, Pralay, 2008. "Theory and inference for regression models with missing responses and covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1302-1331, July.
    11. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    12. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    13. Zhiwei Zhang & Zhen Chen & James F. Troendle & Jun Zhang, 2012. "Causal Inference on Quantiles with an Obstetric Application," Biometrics, The International Biometric Society, vol. 68(3), pages 697-706, September.
    14. 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.
    15. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    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. Bianco, Ana M. & Boente, Graciela & González-Manteiga, Wenceslao & Pérez-González, Ana, 2015. "Robust inference in partially linear models with missing responses," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 88-98.
    2. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    3. Mariela Sued & Marina Valdora & Víctor Yohai, 2020. "Robust doubly protected estimators for quantiles with missing data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 819-843, September.
    4. Wang, Qihua & Härdle, Wolfgang & Linton, Oliver, 2002. "Semiparametric regression analysis under imputation for missing response data," SFB 373 Discussion Papers 2002,6, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Boente, Graciela & Vahnovan, Alejandra, 2017. "Robust estimators in semi-functional partial linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 59-84.
    6. 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.
    7. Zhangong Zhou & Linjun Tang, 2019. "Testing for parametric component of partially linear models with missing covariates," Statistical Papers, Springer, vol. 60(3), pages 747-760, June.
    8. Kim, Kun Ho & Chao, Shih-Kang & Härdle, Wolfgang Karl, 2020. "Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown Function," IRTG 1792 Discussion Papers 2020-008, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    9. 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.
    10. Wang, Xiuli & Zhao, Shengli & Wang, Mingqiu, 2017. "Restricted profile estimation for partially linear models with large-dimensional covariates," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 71-76.
    11. Daniel Becker & Alois Kneip & Valentin Patilea, 2021. "Semiparametric inference for partially linear regressions with Box-Cox transformation," Papers 2106.10723, arXiv.org.
    12. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    13. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    14. Yangxin Huang & Tao Lu, 2017. "Bayesian inference on partially linear mixed-effects joint models for longitudinal data with multiple features," Computational Statistics, Springer, vol. 32(1), pages 179-196, March.
    15. Jun Zhang & Zhenghui Feng & Peirong Xu & Hua Liang, 2017. "Generalized varying coefficient partially linear measurement errors models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 97-120, February.
    16. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    17. Wang, Zhaoliang & Xue, Liugen & Liu, Juanfang, 2019. "Checking nonparametric component for partially nonlinear model with missing response," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 1-8.
    18. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    19. Ana Bianco & Graciela Boente & Wenceslao González-Manteiga & Ana Pérez-González, 2011. "Asymptotic behavior of robust estimators in partially linear models with missing responses: the effect of estimating the missing probability on the simplified marginal estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 524-548, November.
    20. Xin Geng & Carlos Martins-Filho & Feng Yao, 2015. "Estimation of a Partially Linear Regression in Triangular Systems," Working Papers 15-46, Department of Economics, West Virginia University.

    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:testjl:v:28:y:2019:i:1:d:10.1007_s11749-018-0591-5. 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.