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Robust empirical likelihood inference for generalized partial linear models with longitudinal data

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  • Qin, Guoyou
  • Bai, Yang
  • Zhu, Zhongyi

Abstract

In this paper, we propose a robust empirical likelihood (REL) inference for the parametric component in a generalized partial linear model (GPLM) with longitudinal data. We make use of bounded scores and leverage-based weights in the auxiliary random vectors to achieve robustness against outliers in both the response and covariates. Simulation studies demonstrate the good performance of our proposed REL method, which is more accurate and efficient than the robust generalized estimating equation (GEE) method (X. He, W.K. Fung, Z.Y. Zhu, Robust estimation in generalized partial linear models for clustered data, Journal of the American Statistical Association 100 (2005) 1176–1184). The proposed robust method is also illustrated by analyzing a real data set.

Suggested Citation

  • Qin, Guoyou & Bai, Yang & Zhu, Zhongyi, 2012. "Robust empirical likelihood inference for generalized partial linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 32-44.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:32-44
    DOI: 10.1016/j.jmva.2011.08.003
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    References listed on IDEAS

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    1. Qin, Guoyou & Zhu, Zhongyi, 2007. "Robust estimation in generalized semiparametric mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1658-1683, September.
    2. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    3. 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.
    4. Liugen Xue & Lixing Zhu, 2007. "Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data," Biometrika, Biometrika Trust, vol. 94(4), pages 921-937.
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    7. Qin, Guoyou & Bai, Yang & Zhu, Zhongyi, 2009. "Robust empirical likelihood inference for longitudinal data," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2101-2108, October.
    8. Sinha S.K., 2004. "Robust Analysis of Generalized Linear Mixed Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 451-460, January.
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    10. Wang, Qi-Hua & Jing, Bing-Yi, 1999. "Empirical likelihood for partial linear models with fixed designs," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 425-433, February.
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    Citations

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    Cited by:

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    2. Kangning Wang & Lu Lin, 2019. "Robust and efficient estimator for simultaneous model structure identification and variable selection in generalized partial linear varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 60(5), pages 1649-1676, October.
    3. Wang, Kangning & Li, Shaomin & Sun, Xiaofei & Lin, Lu, 2019. "Modal regression statistical inference for longitudinal data semivarying coefficient models: Generalized estimating equations, empirical likelihood and variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 257-276.
    4. Kangning Wang & Wen Shan, 2021. "Copula and composite quantile regression-based estimating equations for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 441-455, June.
    5. Li, Shaomin & Wang, Kangning & Ren, Yanyan, 2018. "Robust estimation and empirical likelihood inference with exponential squared loss for panel data models," Economics Letters, Elsevier, vol. 164(C), pages 19-23.
    6. Kun Chen & Rui Huang, 2021. "Robust empirical likelihood for time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(1), pages 4-18, January.
    7. Tang, Nian-Sheng & Duan, Xing-De, 2014. "Bayesian influence analysis of generalized partial linear mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 86-99.
    8. Bravo, Francesco, 2015. "Semiparametric estimation with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 329-346.
    9. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.
    10. Mozhgan Taavoni & Mohammad Arashi & Samuel Manda, 2023. "Multicollinearity and Linear Predictor Link Function Problems in Regression Modelling of Longitudinal Data," Mathematics, MDPI, vol. 11(3), pages 1-9, January.

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