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Robust inference in generalized partially linear models

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  • Boente, Graciela
  • Rodriguez, Daniela

Abstract

In many situations, data follow a generalized partly linear model in which the mean of the responses is modeled, through a link function, linearly on some covariates and nonparametrically on the remaining ones. A new class of robust estimates for the smooth function [eta], associated to the nonparametric component, and for the parameter , related to the linear one, is defined. The robust estimators are based on a three-step procedure, where large values of the deviance or Pearson residuals are bounded through a score function. These estimators allow us to make easier inferences on the regression parameter and also improve computationally those based on a robust profile likelihood approach. The resulting estimates of turn out to be root-n consistent and asymptotically normally distributed. Besides, the empirical influence function allows us to study the sensitivity of the estimators to anomalous observations. A robust Wald test for the regression parameter is also provided. Through a Monte Carlo study, the performance of the robust estimators and the robust Wald test is compared with that of the classical ones.

Suggested Citation

  • Boente, Graciela & Rodriguez, Daniela, 2010. "Robust inference in generalized partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2942-2966, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:2942-2966
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    1. Qin, Guoyou & Zhu, Zhongyi, 2007. "Robust estimation in generalized semiparametric mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1658-1683, September.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. He, Xuming & Fung, Wing K. & Zhu, Zhongyi, 2005. "Robust Estimation in Generalized Partial Linear Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1176-1184, December.
    4. Liang, Hua, 2006. "Estimation in partially linear models and numerical comparisons," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 675-687, February.
    5. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    6. Bianco, Ana M. & Martínez, Elena, 2009. "Robust testing in the logistic regression model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4095-4105, October.
    7. Chang, Xiao-Wen & Qu, Leming, 2004. "Wavelet estimation of partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 31-48, August.
    8. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    9. Ana Bianco & Graciela Boente & Elena Martínez, 2006. "Robust Tests in Semiparametric Partly Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 435-450, September.
    10. 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.
    11. Vaart,A. W. van der, 1998. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521496032.
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    Cited by:

    1. Claudio Agostinelli & Ana M. Bianco & Graciela Boente, 2020. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 855-893, June.
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    3. Graciela Boente & Daniela Rodriguez, 2012. "Robust estimates in generalized partially linear single-index models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 386-411, June.
    4. Boente, Graciela & Pardo-Fernández, Juan Carlos, 2016. "Robust testing for superiority between two regression curves," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 151-168.
    5. Shen, Chung-Wei & Tsou, Tsung-Shan & Balakrishnan, N., 2011. "Robust likelihood inference for regression parameters in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1696-1714, April.
    6. 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.
    7. Boente, Graciela & Cao, Ricardo & González Manteiga, Wenceslao & Rodriguez, Daniela, 2013. "Testing in generalized partially linear models: A robust approach," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 203-212.
    8. Graciela Boente & Daniela Rodriguez & Pablo Vena, 2020. "Robust estimators in a generalized partly linear regression model under monotony constraints," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 50-89, March.

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