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Estimation in mixed effects model with errors in variables

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  • Cui, Hengjian
  • Ng, Kai W.
  • Zhu, Lixing

Abstract

In this paper, we consider a linear mixed-effects model with measurement errors in both fixed and random effects and find the moment of estimators for the parameters of interest. The strong consistency and asymptotic normality of the estimators are obtained under regularity conditions. Moreover, we obtain the strong consistent estimators of the asymptotic covariance matrices involved in the limiting theory. Simulations are reported for illustration.

Suggested Citation

  • Cui, Hengjian & Ng, Kai W. & Zhu, Lixing, 2004. "Estimation in mixed effects model with errors in variables," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 53-73, October.
    • Handle: RePEc:eee:jmvana:v:91:y:2004:i:1:p:53-73
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    References listed on IDEAS

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    1. Xu-Ping Zhong & Wing-Kam Fung & Bo-Cheng Wei, 2002. "Estimation in Linear Models with Random Effects and Errors-in-Variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 595-606, September.
    2. Lixing Zhu & Hengjian Cui, 2003. "A Semi‐parametric Regression Model with Errors in Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 429-442, June.
    3. Vonesh E. F. & Wang H. & Nie L. & Majumdar D., 2002. "Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 271-283, March.
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    Cited by:

    1. Kheradmandi, Ameneh & Rasekh, Abdolrahman, 2015. "Estimation in skew-normal linear mixed measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 1-11.
    2. Xing-cai Zhou & Jin-Guan Lin, 2014. "Empirical likelihood for varying-coefficient semiparametric mixed-effects errors-in-variables models with longitudinal data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 51-69, March.
    3. Ping Wu & Li Xing Zhu, 2010. "An Orthogonality‐Based Estimation of Moments for Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 253-263, June.
    4. Lili Yue & Jianhong Shi & Jingxuan Luo & Jinguan Lin, 2023. "A Parametric Bootstrap Approach for a One-Way Error Component Regression Model with Measurement Errors," Mathematics, MDPI, vol. 11(19), pages 1-13, October.
    5. Zaixing Li, 2013. "Two kinds of variance/covariance estimates in linear mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 303-324, April.
    6. Karim Zare & Abdolrahman Rasekh & Ali Rasekhi, 2012. "Estimation of variance components in linear mixed measurement error models," Statistical Papers, Springer, vol. 53(4), pages 849-863, November.
    7. Joelmir A. Borssoi & Gilberto A. Paula & Manuel Galea, 2020. "Elliptical linear mixed models with a covariate subject to measurement error," Statistical Papers, Springer, vol. 61(1), pages 31-69, February.
    8. Wangli Xu & Lixing Zhu, 2009. "Kernel‐based Generalized Cross‐validation in Non‐parametric Mixed‐effect Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 229-247, June.

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