Parametric bootstrapping in a generalized extreme value regression model for binary response

TL;DR

This paper applies parametric bootstrapping to a GEV regression model with a binary response, focusing on hypothesis testing and confidence interval estimation for rare event data.

Contribution

It introduces a bootstrap approach for GEV regression models with binary responses, including hypothesis testing and confidence interval estimation.

Findings

Bootstrap method effectively estimates parameter confidence intervals.

The approach improves inference accuracy for rare event modeling.

Application to real data demonstrates practical utility.

Abstract

Generalized extreme value (GEV) regression is often more adapted when we investigate a relationship between a binary response variable $Y$ which represents a rare event and potentiel predictors $\mathbf{X}$. In particular, we use the quantile function of the GEV distribution as link function. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, test of hypothesis) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Bootstrapping estimates the properties of an estimator by measuring those properties when sampling from an approximating distribution. In this paper, we fitted the generalized extreme value regression model, then we performed parametric bootstrap method for testing hupthesis, estimating confidence interval of parameters for generalized extreme value regression model and a real data application.