STATISTICAL INFERENCE IN THE GENERALIZED EXTREME VALUE REGRESSION MODEL BASED ON SIMULATION STUDY

Abstract

Generalized extreme value (GEV) regression model is widely used when the dependent variable $Y$ represents a rare event. In this case the logistic regression model shows relevant drawbacks. 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 $\mathbf X$. Maximum likelihood estimators in this model has been proposed, and their asymptotic properties recently established. We conduct a detailed simulation study of its numerical properties. We evaluate its accuracy and the quality of the normal approximation of its asymptotic distribution. We study the quality of the approximation for constructing asymptotic Wald-type tests of hypothesis. Several others aspects of this model, such as the event probabilities still deserve attention. We also propose estimator of this quantity and we investigate its properties both theoretically and via simulations. Based on these results, we provide recommendations about the range of minimum sample size under which a reliable statistical inference on the event probabilities can be obtained in a GEV regression model. A real-data example illustrates the proposed estimators.