Iterative rank estimation for generalized linear models

• We propose a rank-based quasi-likelihood estimator for generalized linear models.
• Estimation is iterative starting with the nonlinear Wilcoxon estimator.
• Consistency and asymptotic normality of the proposed estimator are established.
• The proposed estimator is robust to outliers in the response space.

In this paper, the estimation of parameters of a generalized linear regression model is considered. The proposed estimator is defined iteratively starting from an initial obtained by minimizing the Wilcoxon dispersion function for independent errors. It is shown that the iterative estimator converges to the rank version of the maximum quasi-likelihood estimator as the number of iterations increases. The consistency and the asymptotic normality of the rank version of the maximum quasi-likelihood estimator are given. As in the linear model, the procedure results in estimators that are robust in the response space. This is proven theoretically via the influence function. A simulation study and a real world data example illustrate the robustness in the response space and efficiency of the estimator.