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Generalized partially linear models with missing covariates

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  • Liang, Hua

Abstract

In this article we study a semiparametric generalized partially linear model when the covariates are missing at random. We propose combining local linear regression with the local quasilikelihood technique and weighted estimating equation to estimate the parameters and nonparameters when the missing probability is known or unknown. We establish normality of the estimators of the parameter and asymptotic expansion for the estimators of the nonparametric part. We apply the proposed models and methods to a study of the relation between virologic and immunologic responses in AIDS clinical trials, in which virologic response is classified into binary variables. We also give simulation results to illustrate our approach.

Suggested Citation

  • Liang, Hua, 2008. "Generalized partially linear models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 880-895, May.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:5:p:880-895
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Hu Yang & Huilan Liu, 2016. "Penalized weighted composite quantile estimators with missing covariates," Statistical Papers, Springer, vol. 57(1), pages 69-88, March.
    3. Nian-Sheng Tang & Pu-Ying Zhao, 2013. "Empirical likelihood semiparametric nonlinear regression analysis for longitudinal data with responses missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 639-665, August.
    4. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2013. "Testing the linear errors-in-variables model with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 875-884.
    5. Jun Jin & Tiefeng Ma & Jiajia Dai & Shuangzhe Liu, 2021. "Penalized weighted composite quantile regression for partially linear varying coefficient models with missing covariates," Computational Statistics, Springer, vol. 36(1), pages 541-575, March.
    6. Linjun Tang & Zhangong Zhou, 2015. "Weighted local linear CQR for varying-coefficient models with missing covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 583-604, September.
    7. Francesco Bravo, 2020. "Robust estimation and inference for general varying coefficient models with missing observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 966-988, December.
    8. Bindele, Huybrechts F., 2018. "Covariates missing at random under signed-rank inference," Econometrics and Statistics, Elsevier, vol. 8(C), pages 78-93.
    9. 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.
    10. Baojiang Chen & Xiao-Hua Zhou, 2013. "Generalized Partially Linear Models for Incomplete Longitudinal Data In the Presence of Population-Level Information," Biometrics, The International Biometric Society, vol. 69(2), pages 386-395, June.
    11. Xue, Liugen & Zhang, Jinghua, 2020. "Empirical likelihood for partially linear single-index models with missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    12. Huilan Liu & Hu Yang & Changgen Peng, 2019. "Weighted composite quantile regression for single index model with missing covariates at random," Computational Statistics, Springer, vol. 34(4), pages 1711-1740, December.
    13. 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.
    14. Song Chen & Ingrid Van Keilegom, 2009. "A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 415-447, November.
    15. Göran Kauermann & Mehboob Ali, 2021. "Semi-parametric regression when some (expensive) covariates are missing by design," Statistical Papers, Springer, vol. 62(4), pages 1675-1696, August.
    16. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.
    17. Bravo, Francesco, 2015. "Semiparametric estimation with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 329-346.
    18. Gressani, Oswaldo & Lambert, Philippe, 2020. "The Laplace-P-spline methodology for fast approximate Bayesian inference in additive partial linear models," LIDAM Discussion Papers ISBA 2020020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Chen, Songxi, 2012. "Estimation in semiparametric models with missing data," MPRA Paper 46216, University Library of Munich, Germany.
    20. 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.
    21. 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.
    22. Guoyou Qin & Zhongyi Zhu & Wing Fung, 2012. "Robust estimation of the generalised partial linear model with missing covariates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 517-530.
    23. Chen, Qixuan & Paik, Myunghee Cho & Kim, Minjin & Wang, Cuiling, 2016. "Using link-preserving imputation for logistic partially linear models with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 174-185.
    24. Chuanhua Wei & Jin Yang, 2020. "Stochastic restricted estimation in partially linear additive errors-in-variables models," Statistical Papers, Springer, vol. 61(3), pages 1269-1279, June.

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