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Empirical likelihood-based dimension reduction inference for linear error-in-responses models with validation study

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  • Wang, Qihua
  • Härdle, Wolfgang

Abstract

In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of Ø with asymptotic normality, the estimated empirical loglikelihoods and the adjusted empirical loglikelihoods for the vector of regression coefficients and linear combinations of the regression coefficients, respectively. The estimated empirical log-likelihoods are shown to be asymptotically distributed as weighted sums of independent Χ21 and the adjusted empirical loglikelihoods are proved to be asymptotically distributed as standard chi-squares, respectively. A simulation study is conducted to compare the proposed methods in terms of coverage accuracies and average lengths of the confidence intervals.

Suggested Citation

  • Wang, Qihua & Härdle, Wolfgang, 2002. "Empirical likelihood-based dimension reduction inference for linear error-in-responses models with validation study," SFB 373 Discussion Papers 2002,82, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200282
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    References listed on IDEAS

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    1. Wang, Qihua, 2000. "Estimation of Linear Error-in-Covariables Models with Validation Data Under Random Censorship," Journal of Multivariate Analysis, Elsevier, vol. 74(2), pages 245-266, August.
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    Cited by:

    1. 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.
    2. Gengsheng Qin & Xiao-Hua Zhou, 2006. "Empirical Likelihood Inference for the Area under the ROC Curve," Biometrics, The International Biometric Society, vol. 62(2), pages 613-622, June.
    3. Xuemei Hu & Xiaohui Liu, 2013. "Empirical likelihood confidence regions for semi-varying coefficient models with linear process errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 161-180, March.
    4. Wang, Qihua & Yu, Keming, 2007. "Likelihood-based kernel estimation in semiparametric errors-in-covariables models with validation data," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 455-480, March.

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