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Empirical likelihood for partly linear models with errors in all variables

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  • Yan, Li
  • Chen, Xia

Abstract

In this paper, we consider the application of the empirical likelihood method to a partly linear model with measurement errors in possibly all the variables. It is shown that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. Also, a class of estimators for the parameter are constructed, and the asymptotic distributions of the proposed estimators are obtained. Some simulations and an application are conducted to illustrate the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:275-288
    DOI: 10.1016/j.jmva.2014.06.007
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    References listed on IDEAS

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    1. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    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. 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.
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    Cited by:

    1. Peixin Zhao & Xiaoshuang Zhou, 2018. "Robust empirical likelihood for partially linear models via weighted composite quantile regression," Computational Statistics, Springer, vol. 33(2), pages 659-674, June.
    2. 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.
    3. Peixin Zhao & Xinrong Tang, 2016. "Imputation based statistical inference for partially linear quantile regression models with missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 991-1009, November.

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