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Robust estimation in partially linear regression models

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  • Yunlu Jiang

Abstract

A new class of robust estimators via the exponential squared loss function with a tuning parameter are presented for the partially linear regression models. Under some conditions, we show that our proposed estimators for the regression parameter can achieve the highest asymptotic breakdown point of . In addition, we propose the data-driven procedure to choose the tuning parameter. Simulation studies are conducted to compare the performances of the proposed method with the existing methods in terms of the bias, standard deviation (Sd) as well as the mean-squared errors (MSE). The results show that our proposed method has smaller Sd and MSE than the existing methods when there are outliers in the dataset. Finally, we apply the proposed method to analyze the Ragweed Pollen Level data and the salinity data, and the results reveal that our method performs better than the existing methods.

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  • Yunlu Jiang, 2015. "Robust estimation in partially linear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2497-2508, November.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:11:p:2497-2508
    DOI: 10.1080/02664763.2015.1043862
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    References listed on IDEAS

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    1. Hamilton, Scott A. & Truong, Young K., 1997. "Local Linear Estimation in Partly Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 1-19, January.
    2. Chang, Xiao-Wen & Qu, Leming, 2004. "Wavelet estimation of partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 31-48, August.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    4. Croux, Christophe & Flandre, Cécile & Haesbroeck, Gentiane, 2002. "The breakdown behavior of the maximum likelihood estimator in the logistic regression model," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 377-386, December.
    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. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    7. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    8. 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.
    9. Xueqin Wang & Yunlu Jiang & Mian Huang & Heping Zhang, 2013. "Robust Variable Selection With Exponential Squared Loss," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 632-643, June.
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    Cited by:

    1. Yunlu Jiang & Guo-Liang Tian & Yu Fei, 2019. "A robust and efficient estimation method for partially nonlinear models via a new MM algorithm," Statistical Papers, Springer, vol. 60(6), pages 2063-2085, December.

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