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Empirical likelihood confidence region for parameter in the errors-in-variables models

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  • Cui, Hengjian
  • Chen, Song Xi

Abstract

This paper proposes a constrained empirical likelihood confidence region for a parameter [beta]0 in the linear errors-in-variables model: Yi=xi[tau][beta]0+[var epsilon]i,Xi=xi+ui,(1[less-than-or-equals, slant]i[less-than-or-equals, slant]n), which is constructed by combining the score function corresponding to the squared orthogonal distance with a constrained region of [beta]0. It is shown that the coverage error of the confidence region is of order n-1, and Bartlett corrections can reduce the coverage errors to n-2. An empirical Bartlett correction is given for practical implementation. Simulations show that the proposed confidence region has satisfactory coverage not only for large samples, but also for small to medium samples.

Suggested Citation

  • Cui, Hengjian & Chen, Song Xi, 2003. "Empirical likelihood confidence region for parameter in the errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 101-115, January.
    • Handle: RePEc:eee:jmvana:v:84:y:2003:i:1:p:101-115
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    References listed on IDEAS

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    1. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    2. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 621-637, December.
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    Cited by:

    1. 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.
    2. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    3. Xuemin Zi & Changliang Zou & Yukun Liu, 2012. "Two-sample empirical likelihood method for difference between coefficients in linear regression model," Statistical Papers, Springer, vol. 53(1), pages 83-93, February.
    4. Hu, Xuemei & Wang, Zhizhong & Zhao, Zhiwei, 2009. "Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1044-1052, April.
    5. Zhong, Pingshou & Cui, Hengjian, 2010. "Empirical likelihood for median regression model with designed censoring variables," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 240-251, January.
    6. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2013. "Testing the linear errors-in-variables model with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 875-884.
    7. Xiuli Wang & Gaorong Li & Lu Lin, 2011. "Empirical likelihood inference for semi-parametric varying-coefficient partially linear EV models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 171-185, March.
    8. Yang, Yiping & Li, Gaorong & Peng, Heng, 2014. "Empirical likelihood of varying coefficient errors-in-variables models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 1-18.
    9. Hu, Xuemei & Wang, Zhizhong & Liu, Feng, 2008. "Zero finite-order serial correlation test in a semi-parametric varying-coefficient partially linear errors-in-variables model," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1560-1569, September.
    10. Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.

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