Maximum likelihood estimation in the generalized extreme value regression model for binary data

Generalized extreme value regression model is widely used when the dependent variable Y represents a rare event. The quantile function of the GEV distribution is used as link function to investigate the relationship between the binary outcome Y and a set of potential predictors X. In this article we develop a maximum likelihood estimation procedure int he generalized extreme value regression model. We establish the asymptotic properties (existence, consistency and asymptotic normality) of the proposed maximum likelihood estimator.