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Instrumental variable-based empirical likelihood inferences for varying-coefficient models with error-prone covariates

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  • Peixin Zhao
  • Liugen Xue

Abstract

This paper presents the empirical likelihood inferences for a class of varying-coefficient models with error-prone covariates. We focus on the case that the covariance matrix of the measurement errors is unknown and neither repeated measurements nor validation data are available. We propose an instrumental variable-based empirical likelihood inference method and show that the proposed empirical log-likelihood ratio is asymptotically chi-squared. Then, the confidence intervals for the varying-coefficient functions are constructed. Some simulation studies and a real data application are used to assess the finite sample performance of the proposed empirical likelihood procedure.

Suggested Citation

  • Peixin Zhao & Liugen Xue, 2013. "Instrumental variable-based empirical likelihood inferences for varying-coefficient models with error-prone covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 380-396, February.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:2:p:380-396
    DOI: 10.1080/02664763.2012.744810
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    1. Jinhong You & Haibo Zhou, 2007. "On Semiparametric EV Models with Serially Correlated Errors in Both Regression Models and Mismeasured Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 365-383, June.
    2. Peixin Zhao & Liugen Xue, 2009. "Empirical likelihood inferences for semiparametric varying-coefficient partially linear errors-in-variables models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 907-923.
    3. Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood for a Varying Coefficient Model With Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 642-654, June.
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    7. Liugen Xue, 2010. "Empirical Likelihood Local Polynomial Regression Analysis of Clustered Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 644-663, December.
    8. Xue, Liugen, 2009. "Empirical likelihood for linear models with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1353-1366, August.
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