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Testing in generalized partially linear models: A robust approach

Author

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  • Boente, Graciela
  • Cao, Ricardo
  • González Manteiga, Wenceslao
  • Rodriguez, Daniela

Abstract

In this paper, we introduce a family of robust statistics which allow to decide between a parametric model and a semiparametric one. More precisely, under a generalized partially linear model, i.e., when the observations satisfy yi|(xi,ti)∼F(⋅,μi) with μi=H(η(ti)+xit β) and H a known link function, we want to test H0:η(t)=α+γt against H1:η is a nonlinear smooth function. A general approach which includes robust estimators based on a robustified deviance or a robustified quasi-likelihood is considered. The asymptotic behavior of the test statistic under the null hypothesis is obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:203-212
    DOI: 10.1016/j.spl.2012.08.031
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    References listed on IDEAS

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    1. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    2. Boente, Graciela & Rodriguez, Daniela, 2010. "Robust inference in generalized partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2942-2966, December.
    3. 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.
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    5. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    6. 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.
    7. Hong‐Tu Zhu & Heping Zhang, 2004. "Hypothesis testing in mixture regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 3-16, February.
    8. Wang, Lan & Qu, Annie, 2007. "Robust Tests in Regression Models With Omnibus Alternatives and Bounded Influence," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 347-358, March.
    9. 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.
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    Cited by:

    1. 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.

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