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Model checking for partially linear models with missing responses at random

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  • 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
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    References listed on IDEAS

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    Cited by:

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    7. 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.
    8. 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.
    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. 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.
    11. 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.
    12. 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.
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    14. 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.
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    17. Bindele, Huybrechts F. & Abebe, Ash, 2015. "Semi-parametric rank regression with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 117-132.
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    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.

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