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A novel robust approach for analysis of longitudinal data

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  • Zhang, Yuexia
  • Qin, Guoyou
  • Zhu, Zhongyi
  • Xu, Wanghong

Abstract

A new robust estimating equation approach for analysis of longitudinal data is developed. To achieve robustness against outliers, a novel approach which corrects the bias induced by outliers through centralizing the covariate matrix in the estimating equation is proposed. The covariates are centralized by subtracting their conditional expectations and the conditional expectations can be estimated by using the local linear smoothing method. The consistency and asymptotic normality of the proposed estimator are established under some regularity conditions. Extensive simulation studies show that the proposed method is robust, has a high efficiency, and is not limited to some specific error distributions. In the end, the proposed method is applied to the longitudinal study of prevalent patients with type 2 diabetes and confirms the effectiveness of dietary fibre intake in reducing glycolated hemoglobin A1c level.

Suggested Citation

  • Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Xu, Wanghong, 2019. "A novel robust approach for analysis of longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 83-95.
    • Handle: RePEc:eee:csdana:v:138:y:2019:i:c:p:83-95
    DOI: 10.1016/j.csda.2019.04.002
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    References listed on IDEAS

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    1. He, Xuming & Fung, Wing K. & Zhu, Zhongyi, 2005. "Robust Estimation in Generalized Partial Linear Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1176-1184, December.
    2. 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.
    3. McCann, Lauren & Welsch, Roy E., 2007. "Robust variable selection using least angle regression and elemental set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 249-257, September.
    4. Yanyuan Ma & Liping Zhu, 2013. "Doubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 305-322, March.
    5. Xuerong Chen & Alan T. K. Wan & Yong Zhou, 2015. "Efficient Quantile Regression Analysis With Missing Observations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 723-741, June.
    6. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    7. Lv, Jing & Yang, Hu & Guo, Chaohui, 2015. "An efficient and robust variable selection method for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 74-88.
    8. Weiping Zhang & Chenlei Leng & Cheng Yong Tang, 2015. "A joint modelling approach for longitudinal studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 219-238, January.
    9. She, Yiyuan & Owen, Art B., 2011. "Outlier Detection Using Nonconvex Penalized Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 626-639.
    10. John S. Preisser & Bahjat F. Qaqish, 1999. "Robust Regression for Clustered Data with Application to Binary Responses," Biometrics, The International Biometric Society, vol. 55(2), pages 574-579, June.
    11. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    12. Jeng‐Min Chiou & Hans‐Georg Müller, 2005. "Estimated estimating equations: semiparametric inference for clustered and longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 531-553, September.
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    Cited by:

    1. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Zhang, Jiajia, 2022. "Empirical likelihood inference for longitudinal data with covariate measurement errors: An application to the LEAN study," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).

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