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Robust estimation in partially linear errors-in-variables models

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  • Bianco, Ana M.
  • Spano, Paula M.

Abstract

In many applications of regression analysis, there are covariates that are measured with errors. A robust family of estimators of the parametric and nonparametric components of a structural partially linear errors-in-variables model is introduced. The proposed estimators are based on a three-step procedure where robust orthogonal regression estimators are combined with robust smoothing techniques. Under regularity conditions, it is proved that the resulting estimators are consistent. The robustness of the proposal is studied by means of the empirical influence function when the linear parameter is estimated using the orthogonal M-estimator. A simulation study allows to compare the behaviour of the robust estimators with their classical relatives and a real example data is analysed to illustrate the performance of the proposal.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:106:y:2017:i:c:p:46-64
    DOI: 10.1016/j.csda.2016.09.002
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    References listed on IDEAS

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    1. Ana Bianco & Graciela Boente, 2007. "Robust estimators under semi‐parametric partly linear autoregression: Asymptotic behaviour and bandwidth selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 274-306, March.
    2. Wang, Qihua & Sun, Zhihua, 2007. "Estimation in partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1470-1493, August.
    3. Maronna, Ricardo A. & Yohai, Victor J., 2010. "Correcting MM estimates for "fat" data sets," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3168-3173, December.
    4. Liang, Hua & Li, Runze, 2009. "Variable Selection for Partially Linear Models With Measurement Errors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 234-248.
    5. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    6. Christophe Croux & Mohammed Fekri & Anne Ruiz-Gazen, 2010. "Fast and robust estimation of the multivariate errors in variables model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 286-303, August.
    7. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    8. Fekri, M. & Ruiz-Gazen, A., 2004. "Robust weighted orthogonal regression in the errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 89-108, January.
    9. 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.
    10. Boente, Graciela & Rodriguez, Daniela, 2010. "Robust inference in generalized partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2942-2966, December.
    11. Hua Liang & Suojin Wang & Raymond J. Carroll, 2007. "Partially linear models with missing response variables and error-prone covariates," Biometrika, Biometrika Trust, vol. 94(1), pages 185-198.
    12. 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.
    13. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    14. Härdle, Wolfgang, 1984. "Robust regression function estimation," Journal of Multivariate Analysis, Elsevier, vol. 14(2), pages 169-180, April.
    15. Ma, Yanyuan & Carroll, Raymond J., 2006. "Locally Efficient Estimators for Semiparametric Models With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1465-1474, December.
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