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Projeto de investigação
Modelação de Acontecimentos Raros: Revisitando Problemas em Aberto em Estatística de Extremos
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Contributions to inference in extremes based on moment type statistics
Publication . Silva Lomba, Jessica; Alves, Maria Isabel Fraga; Neves, Cláudia Margarida Pedrosa
Extreme Value Theory and Statistics constitute the ideal toolbox to handle rare and extreme events,
for which inference through classical Gaussianbased methodologies is unreliable. In this thesis,
we start by reviewing the basis of Statistics of Extremes and statistical moments, then diving into
open topics from a methodological standpoint, supported by simulation studies of the proposed
contributions’ properties, together with illustrative analysis of data from several applied fields.
Three new methods for appropriate threshold selection are suggested, developed under the Gen eralized Pareto and peaksoverthreshold parametric framework for univariate, independent and
identically distributed data. The proposed Automatic Lmoment Ratio Selection Method stands out
as the superior technique, being automatic, objective and computationally effective while presenting
overall good performance compared to stateoftheart alternatives. Data sets of significant wave
heights are considered, and results compared to previously existing studies of this data. Further,
an analysis of very small data sets of measurements of Giant Squids is conducted with the aim of
estimating the species’ maximum possible size – a novelty Extremesdriven take on this problem
from the field of Zoology.
This work moreover describes how the known semiparametric mixed moment estimator for the
Extreme Value Index may be used in the context of multivariate data, pooled across space and time.
The setup considers the presence of extreme spatial dependence and a possibly nonmonotonic trend
in the frequency of extremes through both space and/or time (heteroscedasticity). The asymptotic
properties of the estimator are derived under this more complex scenario, and its application is
illustrated through the study of reanalysis daily precipitation series recorded for a set of locations in
homogeneous regions of the United Kingdom. The estimators performance is compared with that
of the common benchmark maximum likelihood estimator under the same conditions, and found to
be generally favorable.
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Entidade financiadora
Fundação para a Ciência e a Tecnologia
Programa de financiamento
OE
Número da atribuição
SFRH/BD/130764/2017