The Role of Bootstrap Methodologies in the Estimation of a Negative Extreme Value Index

In this note we deal with the estimation, under a semi-parametric framework, of a negative extreme value index, the primary parameter in statistics of extremes. We consider a recent class of generalized negative moment estimators of a negative extreme value index. Apart from the usual integer parameter k, related to the number of top order statistics involved in the estimation, the estimator depend on an extra real parameter θ, which makes it highly flexible and possibly second-order unbiased for a large variety of models. We are interested on the study of the bootstrap method in Gomes et al. (2013) for the adaptive choice of the parameters.