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Name: Maria Ivette Gomes

Talk Title: A few Progresses in Statistics of Extremes through the use of Generalized Means

Abstract: Statistics of extremes, either univariate or multivariate, have been recently faced with many challenges, especially the ones related to topics like risk modelling of big data and robustness of the methodologies that enable to understand the complexity of extreme events in the most diverse areas of applications. In statistical extreme value theory (EVT), generalized means (GMs) have recently been used with success in the estimation of a positive extreme value index (EVI). Due to the specificity of the Weibull tail coefficient (WTC), its relevance and its deep link to a positive EVI, we shall now make use of GMs in the estimation of the WTC, also crucial for an adequate risk assessment. Regarding the mean-of-order-p estimation, we could always find a value of p (negative, contrarily to what happens with the mean-of-order-p EVI- estimation), such that, for adequate values of the threshold, there is a reduction in mean square error, as well as in bias. The lack of efficiency of the mean-of-order-p WTC-estimators for positive p, and of the mean-of-order-p EVI-estimators for negative p, together with results related to the robustness of the mean-of-order-p EVI-estimators associated with p=-1, deserves a further discussion of the topic ‘robustness versus efficiency’. 

This talk is a contributed talk at EVA 2021. View the programme here.