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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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    References listed on IDEAS

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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. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
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    5. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.

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