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A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error


  • Grace Y. Yi
  • Yanyuan Ma
  • Raymond J. Carroll


Covariate measurement error and missing responses are typical features in longitudinal data analysis. There has been extensive research on either covariate measurement error or missing responses, but relatively little work has been done to address both simultaneously. In this paper, we propose a simple method for the marginal analysis of longitudinal data with time-varying covariates, some of which are measured with error, while the response is subject to missingness. Our method has a number of appealing properties: assumptions on the model are minimal, with none needed about the distribution of the mismeasured covariate; implementation is straightforward and its applicability is broad. We provide both theoretical justification and numerical results. Copyright 2012, Oxford University Press.

Suggested Citation

  • Grace Y. Yi & Yanyuan Ma & Raymond J. Carroll, 2012. "A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error," Biometrika, Biometrika Trust, vol. 99(1), pages 151-165.
  • Handle: RePEc:oup:biomet:v:99:y:2012:i:1:p:151-165

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    References listed on IDEAS

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    2. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
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    4. Horowitz, Joel L, 2001. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Econometrica, Econometric Society, vol. 69(2), pages 499-513, March.
    5. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-137, January.
    6. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710.
    7. Fermanian, Jean-David, 2003. "Nonparametric estimation of competing risks models with covariates," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 156-191, April.
    8. Joel L. Horowitz, 1999. "Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 67(5), pages 1001-1028, September.
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    Cited by:

    1. Jun Zhang & Zhenghui Feng & Peirong Xu & Hua Liang, 2017. "Generalized varying coefficient partially linear measurement errors models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 97-120, February.
    2. repec:eee:csdana:v:121:y:2018:i:c:p:104-112 is not listed on IDEAS
    3. Yih-Huei Huang & Chi-Chung Wen & Yu-Hua Hsu, 2015. "The Extensively Corrected Score for Measurement Error Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 911-924, December.
    4. Qin, Guoyou & Zhang, Jiajia & Zhu, Zhongyi, 2016. "Simultaneous mean and covariance estimation of partially linear models for longitudinal data with missing responses and covariate measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 24-39.

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