Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators |
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Authors: | María Jaenada Leandro Pardo |
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Institution: | Department of Statistics and Operation Research, Faculty of Mathematics, Complutense University of Madrid, Plaza Ciencias, 3, 28040 Madrid, Spain; |
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Abstract: | Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests. |
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Keywords: | generalized linear model independent and nonidentically distributed observations minimum Ré nyi’ s pseudodistance estimators robust Wald-type test statistics for GLMs influence function for GLMs poisson regression model |
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