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Abstract:
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In this paper, we consider the estimation of parameters of a double generalized linear model in which both the mean and the variance are allowed to depend on explanatory variables. The proposed estimation technique is conducted in a two-step process, iterating between the estimation of the mean and that of the variance by minimizing a rank based objective function, similar to the one in Miakonkana et al (2014), at each step. This extends the estimation method proposed in Miakonkana et al (2014) to generalized linear models with unknown variance structure, yielding more flexibility in the model. Unlike the maximum likelihood based double generalized linear models, the proposed estimator is robust to outliers in the response. In addition the proposed estimator inherits theoretical properties, that is, consistency and asymptotic normality, of the estimators developed in Miakonkana et al (2014). It is shown through a simulation study and a real world data example that the rank based estimator is more robust than the maximum likelihood based estimators, in the sense of being less sensitive to perturbations in the response of either the mean or the variance model.
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