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Nonparametric checks for varying coefficient models with missing response at random

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  • Wangli Xu
  • Xu Guo

Abstract

In this paper, we propose a test on the parametric form of the coefficient functions in the varying coefficient model with missing response. Two groups of completed data sets are constructed by using imputation and inverse probability weighting methods respectively. By noting that the coefficient part can be a regression function for a specific model, we construct two empirical process-based tests. The asymptotical distributions of the proposed tests under null and local alternative hypothesis are investigated respectively. Simulation study is carried out to show the power performance of the test. We illustrate the proposed approaches with an environmental data set. Copyright Springer-Verlag 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:4:p:459-482
    DOI: 10.1007/s00184-012-0399-3
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    4. 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.
    5. Wang-Li Xu & Li-Xing Zhu, 2009. "A goodness-of-fit test for a varying-coefficients model in longitudinal studies," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 427-440.
    6. Jianqing Fan & Wenyang Zhang, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying‐coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731, December.
    7. Wang-Li Xu & Li-Xing Zhu, 2008. "Goodness-of-fit testing for varying-coefficient models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 129-146, September.
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    Cited by:

    1. Yu-Ye Zou & Han-Ying Liang & Jing-Jing Zhang, 2015. "Nonlinear wavelet density estimation with data missing at random when covariates are present," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 967-995, November.
    2. 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.
    3. Guo, Xu & Song, Lianlian & Fang, Yun & Zhu, Lixing, 2019. "Model checking for general linear regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 1-12.

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