Extreme Value Theory (EVT) and
Applications
The
existing
estimators in extreme value theory suffer from high bias and variance.
In some
cases a reduction of these values was attained.
We expect to continue developing and studying, both asymptotically and
by Monte Carlo methods, estimators of parameters and other related
quantities in modeling rare events – e.g. the tail index, the extremal
index, high quantiles and probability of failure sets – both in an
independence and in a dependence framework. We also aim to apply the
theoretical results to real data, in a joint work with researchers
belonging to other Units in the university.
The application of the generalized jackknife methodology has proved to
result in the bias reduction of estimators of the tail index in heavy
tailed models. We aim to extend the application of this methodology to
estimators defined in a broader class of distributions. The kernel
estimators used in density estimation and in smoothing may also be
applied as a flexible tool to reduce bias and/or volatility.
The analysis of dependence regarded in a temporal or spatial approach
in univariate and multivariate EVT is also of interest. We are
particularly interested in problems like the estimation of the extremal
index, involving bootstrap techniques, and modeling dependence and
asymptotic dependence.
Possible applications are e.g. in environmental problems, like large
fires and hydrology data, as well as in finance and insurance.
Members:
Ana Ferreira
Henriques
M. João
Martins
M. Manuela Neves
Figueiredo