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Testing the adequacy of varying coefficient models with missing responses at random

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  • Wangli Xu
  • Lixing Zhu

Abstract

In this paper, we investigate checking the adequacy of varying coefficient models with response missing at random. In doing so, we first construct two completed data sets based on imputation and marginal inverse probability weighted methods, respectively. The empirical process-based tests by using these two completed data sets are suggested and the asymptotic properties of the test statistics under the null and local alternative hypotheses are studied. Because the limiting null distribution is intractable, a Monte Carlo approach is applied to approximate the distribution to determine critical values. Simulation studies are carried out to examine the performance of our method, and a real data set from an environmental study is analyzed for illustration. Copyright Springer-Verlag 2013

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  • 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.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:1:p:53-69
    DOI: 10.1007/s00184-011-0375-3
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    References listed on IDEAS

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    1. Chiang C-T. & Rice J. A & Wu C. O, 2001. "Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 605-619, June.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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. 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. 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.
    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.

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