62 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 spliced Gamma-Generalized Pareto model for short-term extreme wind speed probabilistic forecasting
Renewable sources of energy such as wind power have become a sustainable
alternative to fossil fuel-based energy. However, the uncertainty and
fluctuation of the wind speed derived from its intermittent nature bring a
great threat to the wind power production stability, and to the wind turbines
themselves. Lately, much work has been done on developing models to forecast
average wind speed values, yet surprisingly little has focused on proposing
models to accurately forecast extreme wind speeds, which can damage the
turbines. In this work, we develop a flexible spliced Gamma-Generalized Pareto
model to forecast extreme and non-extreme wind speeds simultaneously. Our model
belongs to the class of latent Gaussian models, for which inference is
conveniently performed based on the integrated nested Laplace approximation
method. Considering a flexible additive regression structure, we propose two
models for the latent linear predictor to capture the spatio-temporal dynamics
of wind speeds. Our models are fast to fit and can describe both the bulk and
the tail of the wind speed distribution while producing short-term extreme and
non-extreme wind speed probabilistic forecasts.Comment: 25 page
Likelihood estimators for multivariate extremes
The main approach to inference for multivariate extremes consists in
approximating the joint upper tail of the observations by a parametric family
arising in the limit for extreme events. The latter may be expressed in terms
of componentwise maxima, high threshold exceedances or point processes,
yielding different but related asymptotic characterizations and estimators. The
present paper clarifies the connections between the main likelihood estimators,
and assesses their practical performance. We investigate their ability to
estimate the extremal dependence structure and to predict future extremes,
using exact calculations and simulation, in the case of the logistic model
Modeling Spatial Dependence with Cauchy Convolution Processes
We study the class of dependence models for spatial data obtained from Cauchy
convolution processes based on different types of kernel functions. We show
that the resulting spatial processes have appealing tail dependence properties,
such as tail dependence at short distances and independence at long distances
with suitable kernel functions. We derive the extreme-value limits of these
processes, study their smoothness properties, and detail some interesting
special cases. To get higher flexibility at sub-asymptotic levels and
separately control the bulk and the tail dependence properties, we further
propose spatial models constructed by mixing a Cauchy convolution process with
a Gaussian process. We demonstrate that this framework indeed provides a rich
class of models for the joint modeling of the bulk and the tail behaviors. Our
proposed inference approach relies on matching model-based and empirical
summary statistics, and an extensive simulation study shows that it yields
accurate estimates. We demonstrate our new methodology by application to a
temperature dataset measured at 97 monitoring stations in the state of
Oklahoma, US. Our results indicate that our proposed model provides a very good
fit to the data, and that it captures both the bulk and the tail dependence
structures accurately.Comment: 36 pages, 7 figure
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