IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i4p636-651.html
   My bibliography  Save this article

Model checking for partially linear models with missing responses at random

Author

Listed:
  • Sun, Zhihua
  • Wang, Qihua
  • Dai, Pengjie

Abstract

In this paper, we investigate the model checking problem for a partial linear model while some responses are missing at random. By imputation and marginal inverse probability weighted methods, two completed data sets are constructed. Based on the two completed data sets, we build two empirical process-based tests for examining the adequacy of partial linearity of the model. The asymptotic distributions of the test statistics under the null hypothesis and local alternative hypotheses are obtained respectively. A re-sampling approach is applied to obtain the approximation to the null distributions of the test statistics. Simulation results show that the proposed tests work well and both proposed methods have better finite sample properties compared with the complete case (CC) analysis which discards all the subjects with missing data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:4:p:636-651
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00164-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Dikta, Gerhard & Kvesic, Marsel & Schmidt, Christian, 2006. "Bootstrap Approximations in Model Checks for Binary Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 521-530, June.
    3. Wang, Qihua & Yu, Keming, 2007. "Likelihood-based kernel estimation in semiparametric errors-in-covariables models with validation data," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 455-480, March.
    4. C. Y. Wang & Hua Yun Chen, 2001. "Augmented Inverse Probability Weighted Estimator for Cox Missing Covariate Regression," Biometrics, The International Biometric Society, vol. 57(2), pages 414-419, June.
    5. D. Y. Lin & L. J. Wei & Z. Ying, 2002. "Model-Checking Techniques Based on Cumulative Residuals," Biometrics, The International Biometric Society, vol. 58(1), pages 1-12, March.
    6. Whang, Yoon-Jae & Andrews, Donald W. K., 1993. "Tests of specification for parametric and semiparametric models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 277-318.
    7. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(4), pages 435-451, December.
    8. 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.
    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. Andrew Gelman & Iven Van Mechelen & Geert Verbeke & Daniel F. Heitjan & Michel Meulders, 2005. "Multiple Imputation for Model Checking: Completed-Data Plots with Missing and Latent Data," Biometrics, The International Biometric Society, vol. 61(1), pages 74-85, March.
    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. 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.
    2. Jun Wang & Dianpeng Wang & Yubin Tian, 2022. "Multidimensional specification test based on non-stationary time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 348-372, June.
    3. 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.
    4. 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.
    5. Bindele, Huybrechts F. & Abebe, Ash, 2015. "Semi-parametric rank regression with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 117-132.
    6. Cui, Li-E & Zhao, Puying & Tang, Niansheng, 2022. "Generalized empirical likelihood for nonsmooth estimating equations with missing data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    7. Sun, Zhihua & Ye, Xue & Sun, Liuquan, 2015. "Consistent test of error-in-variables partially linear model with auxiliary variables," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 118-131.
    8. Zhihua Sun & Dongshan Luo & Xiaohua Zhou & Qingzhao Zhang, 2021. "Comparative studies on the adequacy check of parametric measurement error models with auxiliary variable," Statistical Papers, Springer, vol. 62(4), pages 1723-1751, August.
    9. Fayyaz Bahari & Safar Parsi & Mojtaba Ganjali, 2021. "Goodness of fit test for general linear model with nonignorable missing on response variable," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 163-196, March.
    10. Xu Guo & Wangli Xu & Lixing Zhu, 2015. "Model checking for parametric regressions with response missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 229-259, April.
    11. 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.
    12. 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.
    13. Tianfa Xie & Zhihua Sun & Liuquan Sun, 2012. "A consistent model specification test for a partial linear model with covariates missing at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 841-856, December.
    14. Heng Lian, 2011. "Functional partial linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 115-128.
    15. 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.
    16. 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.
    17. Ning, Zijun & Tang, Linjun, 2014. "Estimation and test procedures for composite quantile regression with covariates missing at random," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 15-25.
    18. Wangli Xu & Xu Guo, 2013. "Checking the adequacy of partial linear models with missing covariates at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 473-490, June.
    19. Wangli Xu & Xu Guo & Lixing Zhu, 2012. "Goodness-of-fitting for partial linear model with missing response at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 103-118.
    20. 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.

    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. Wangli Xu & Xu Guo & Lixing Zhu, 2012. "Goodness-of-fitting for partial linear model with missing response at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 103-118.
    2. Majid Mojirsheibani & Timothy Reese, 2017. "Kernel regression estimation for incomplete data with applications," Statistical Papers, Springer, vol. 58(1), pages 185-209, March.
    3. Nengxiang Ling & Rui Kan & Philippe Vieu & Shuyu Meng, 2019. "Semi-functional partially linear regression model with responses missing at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 39-70, January.
    4. Nengxiang Ling & Lilei Cheng & Philippe Vieu & Hui Ding, 2022. "Missing responses at random in functional single index model for time series data," Statistical Papers, Springer, vol. 63(2), pages 665-692, April.
    5. 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.
    6. Shuanghua Luo & Cheng-yi Zhang, 2016. "Nonparametric $$M$$ M -type regression estimation under missing response data," Statistical Papers, Springer, vol. 57(3), pages 641-664, September.
    7. 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.
    8. Bindele, Huybrechts F., 2018. "Covariates missing at random under signed-rank inference," Econometrics and Statistics, Elsevier, vol. 8(C), pages 78-93.
    9. 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.
    10. 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.
    11. Yan-Ting Xiao & Fu-Xiao Li, 2020. "Estimation in partially linear varying-coefficient errors-in-variables models with missing response variables," Computational Statistics, Springer, vol. 35(4), pages 1637-1658, December.
    12. 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.
    13. Bindele, Huybrechts F. & Abebe, Ash, 2015. "Semi-parametric rank regression with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 117-132.
    14. 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.
    15. Chen, Songxi, 2012. "Estimation in semiparametric models with missing data," MPRA Paper 46216, University Library of Munich, Germany.
    16. 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.
    17. Wangli Xu & Xu Guo, 2013. "Checking the adequacy of partial linear models with missing covariates at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 473-490, June.
    18. Zhongqi Liang & Qihua Wang, 2023. "A robust model averaging approach for partially linear models with responses missing at random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(4), pages 1933-1952, December.
    19. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.
    20. 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.

    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:100:y:2009:i:4:p:636-651. 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.