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Empirical Likelihood Confidence Region for Parameters in Semi‐linear Errors‐in‐Variables Models

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  • HENGJIAN CUI
  • EFANG KONG

Abstract

. This paper proposes a constrained empirical likelihood confidence region for a parameter in the semi‐linear errors‐in‐variables model. The confidence region is constructed by combining the score function corresponding to the squared orthogonal distance with a constraint on the parameter, and it overcomes that the solution of limiting mean estimation equations is not unique. It is shown that the empirical log likelihood ratio at the true parameter converges to the standard chi‐square distribution. Simulations show that the proposed confidence region has coverage probability which is closer to the nominal level, as well as narrower than those of normal approximation of generalized least squares estimator in most cases. A real data example is given.

Suggested Citation

  • Hengjian Cui & Efang Kong, 2006. "Empirical Likelihood Confidence Region for Parameters in Semi‐linear Errors‐in‐Variables Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 153-168, March.
    • Handle: RePEc:bla:scjsta:v:33:y:2006:i:1:p:153-168
    DOI: 10.1111/j.1467-9469.2006.00468.x
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    Cited by:

    1. Jianhong Shi & Fanrong Zhao, 2018. "Statistical inference for heteroscedastic semi-varying coefficient EV models under restricted condition," Statistical Papers, Springer, vol. 59(2), pages 487-511, June.
    2. Zhang, Junhua & Feng, Sanying & Li, Gaorong & Lian, Heng, 2011. "Empirical likelihood inference for partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 113(2), pages 165-167.
    3. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.
    4. Bianco, Ana M. & Spano, Paula M., 2017. "Robust estimation in partially linear errors-in-variables models," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 46-64.
    5. 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.
    6. Guo-Liang Fan & Han-Ying Liang & Jiang-Feng Wang, 2013. "Empirical likelihood for heteroscedastic partially linear errors-in-variables model with α-mixing errors," Statistical Papers, Springer, vol. 54(1), pages 85-112, February.
    7. Cui, Hengjian & Hu, Tao, 2011. "On nonlinear regression estimator with denoised variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1137-1149, February.
    8. Yan, Li & Chen, Xia, 2014. "Empirical likelihood for partly linear models with errors in all variables," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 275-288.
    9. Sun, Zhimeng & Zhang, Zhongzhan, 2013. "Semiparametric analysis of additive isotonic errors-in-variables regression models," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 100-114.
    10. Huang, Zhensheng, 2012. "Empirical likelihood for the parametric part in partially linear errors-in-function models," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 63-66.
    11. Xia Chen & Liyue Mao, 2020. "Penalized empirical likelihood for partially linear errors-in-variables models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 597-623, December.
    12. Amjad D. Al-Nasser, 2014. "Two steps generalized maximum entropy estimation procedure for fitting linear regression when both covariates are subject to error," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1708-1720, August.

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