A robust hurdle poisson model in the estimation of the extremal index

Abstract

In statistical extreme value theory, the occurrence of clusters of exceedances above a high threshold is related to the extremal index (EI), when that parameter exists. In such cases, the EI represents the reciprocal of the mean cluster dimension in the limit distribution. The set of observed cluster sizes may contain too many zeroes, depending on the scheme used in the identification of the clusters and posterior estimation process, as it happens with the Blocks estimator. We consider the estimation of the mean cluster size by modelling the clusters dimension with a hurdle zero truncated Poisson regression model. The goal is to find a robust estimator with a good performance along increasing quantiles and computationally user friendly. The paper highlights the importance of the last question also, since many statisticians use or do not use some methods, depending on the free software devoted to the method and respective confidence in their optimization procedures and results. A simulation study explores and compares different proposals.