2,093 research outputs found
Local likelihood estimation of complex tail dependence structures, applied to U.S. precipitation extremes
To disentangle the complex non-stationary dependence structure of
precipitation extremes over the entire contiguous U.S., we propose a flexible
local approach based on factor copula models. Our sub-asymptotic spatial
modeling framework yields non-trivial tail dependence structures, with a
weakening dependence strength as events become more extreme, a feature commonly
observed with precipitation data but not accounted for in classical asymptotic
extreme-value models. To estimate the local extremal behavior, we fit the
proposed model in small regional neighborhoods to high threshold exceedances,
under the assumption of local stationarity, which allows us to gain in
flexibility. Adopting a local censored likelihood approach, inference is made
on a fine spatial grid, and local estimation is performed by taking advantage
of distributed computing resources and the embarrassingly parallel nature of
this estimation procedure. The local model is efficiently fitted at all grid
points, and uncertainty is measured using a block bootstrap procedure. An
extensive simulation study shows that our approach can adequately capture
complex, non-stationary dependencies, while our study of U.S. winter
precipitation data reveals interesting differences in local tail structures
over space, which has important implications on regional risk assessment of
extreme precipitation events
A multivariate piecing-together approach with an application to operational loss data
The univariate piecing-together approach (PT) fits a univariate generalized
Pareto distribution (GPD) to the upper tail of a given distribution function in
a continuous manner. We propose a multivariate extension. First it is shown
that an arbitrary copula is in the domain of attraction of a multivariate
extreme value distribution if and only if its upper tail can be approximated by
the upper tail of a multivariate GPD with uniform margins. The multivariate PT
then consists of two steps: The upper tail of a given copula is cut off and
substituted by a multivariate GPD copula in a continuous manner. The result is
again a copula. The other step consists of the transformation of each margin of
this new copula by a given univariate distribution function. This provides,
altogether, a multivariate distribution function with prescribed margins whose
copula coincides in its central part with and in its upper tail with a GPD
copula. When applied to data, this approach also enables the evaluation of a
wide range of rational scenarios for the upper tail of the underlying
distribution function in the multivariate case. We apply this approach to
operational loss data in order to evaluate the range of operational risk.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ343 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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