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

Ayanendranath Basu (), Abhik Ghosh (), Abhijit Mandal (), Nirian Martin () and Leandro Pardo ()
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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

Statistical Methods & Applications, 2021, vol. 30, issue 3, No 10, 973-1005

Abstract: 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.

Keywords: Generalized linear models; Minimum density power divergence estimator; Wald-type tests; Robustness (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10260-020-00544-4

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