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Robust Wald-type tests in GLM with random design based on minimum density power divergence estimators

Author

Listed:
  • Ayanendranath Basu

    (Indian Statistical Institute)

  • Abhik Ghosh

    (Indian Statistical Institute)

  • Abhijit Mandal

    (Wayne State University)

  • Nirian Martin

    (Complutense University of Madrid)

  • Leandro Pardo

    (Complutense University of Madrid)

Abstract

We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use this estimator to propose robust Wald-type tests for testing any general composite null hypothesis about the GLM. The asymptotic and robustness properties of the proposed tests are also examined for the GLM with random design. Application of the proposed robust inference procedures to the popular Poisson regression model for analyzing count data is discussed in detail both theoretically and numerically through simulation studies and real data examples.

Suggested Citation

  • Ayanendranath Basu & Abhik Ghosh & Abhijit Mandal & Nirian Martin & Leandro Pardo, 2021. "Robust Wald-type tests in GLM with random design based on minimum density power divergence estimators," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 973-1005, September.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:3:d:10.1007_s10260-020-00544-4
    DOI: 10.1007/s10260-020-00544-4
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    References listed on IDEAS

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    1. Ghosh, Abhik & Mandal, Abhijit & Martín, Nirian & Pardo, Leandro, 2016. "Influence analysis of robust Wald-type tests," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 102-126.
    2. Alfio Marazzi & Marina Valdora & Victor Yohai & Michael Amiguet, 2019. "A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 223-241, March.
    3. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    4. William H. Aeberhard & Eva Cantoni & Stephane Heritier, 2014. "Robust inference in the negative binomial regression model with an application to falls data," Biometrics, The International Biometric Society, vol. 70(4), pages 920-931, December.
    5. 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.
    6. Bianco, Ana M. & Boente, Graciela & Rodrigues, Isabel M., 2013. "Robust tests in generalized linear models with missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 80-97.
    7. Croux, Christophe & Haesbroeck, Gentiane, 2003. "Implementing the Bianco and Yohai estimator for logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 273-295, October.
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