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A Semi‐parametric Regression Model with Errors in Variables

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  • Lixing Zhu
  • Hengjian Cui

Abstract

. In this paper, we consider a partial linear regression model with measurement errors in possibly all the variables. We use a method of moments and deconvolution to construct a new class of parametric estimators together with a non‐parametric kernel estimator. Strong convergence, optimal rate of weak convergence and asymptotic normality of the estimators are investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:2:p:429-442
    DOI: 10.1111/1467-9469.00340
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    Citations

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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. Cui, Hengjian & Ng, Kai W. & Zhu, Lixing, 2004. "Estimation in mixed effects model with errors in variables," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 53-73, October.
    3. 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.
    4. Bang-Qiang He & Xing-Jian Hong & Guo-Liang Fan, 2020. "Penalized empirical likelihood for partially linear errors-in-variables panel data models with fixed effects," Statistical Papers, Springer, vol. 61(6), pages 2351-2381, December.
    5. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.
    6. Leise Kelli de Oliveira & Gracielle Gonçalves Ferreira de Araújo & Bruno Vieira Bertoncini & Carlos David Pedrosa & Francisco Gildemir Ferreira da Silva, 2022. "Modelling Freight Trip Generation Based on Deliveries for Brazilian Municipalities," Sustainability, MDPI, vol. 14(16), pages 1-18, August.
    7. 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.
    8. 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.
    9. Haibo Zhou & Jinhong You & Bin Zhou, 2010. "Statistical inference for fixed-effects partially linear regression models with errors in variables," Statistical Papers, Springer, vol. 51(3), pages 629-650, September.
    10. Yanqin Feng & Ling Ma & Jianguo Sun, 2015. "Regression Analysis of Current Status Data Under the Additive Hazards Model with Auxiliary Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 118-136, March.

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