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Methods of Tail Dependence Estimation
Characterization and quantification of climate extremes and their dependencies are fundamental to the studying of natural hazards. This chapter reviews various parametric and nonparametric tail dependence coefficient estimators. The tail dependence coefficient describes the dependence (degree of association) between concurrent extremes at different locations. Accurate and reliable knowledge of the spatial characteristics of extremes can help improve the existing methods of modeling the occurrence probabilities of extreme events. This chapter will review these methods and use two case studies to demonstrate the application of tail dependence analysis
Approximate Bayesian inference in semiparametric copula models
We describe a simple method for making inference on a functional of a
multivariate distribution. The method is based on a copula representation of
the multivariate distribution and it is based on the properties of an
Approximate Bayesian Monte Carlo algorithm, where the proposed values of the
functional of interest are weighed in terms of their empirical likelihood. This
method is particularly useful when the "true" likelihood function associated
with the working model is too costly to evaluate or when the working model is
only partially specified.Comment: 27 pages, 18 figure
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure
among variables and to generate joint distributions by combining given marginal
distributions. Simulations play a relevant role in finance and insurance. They are used to
replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so
on. Using copulas, it is easy to construct and simulate from multivariate distributions based
on almost any choice of marginals and any type of dependence structure. In this paper we
outline recent contributions of statistical modeling using copulas in finance and insurance.
We review issues related to the notion of copulas, copula families, copula-based dynamic and
static dependence structure, copulas and latent factor models and simulation of copulas.
Finally, we outline hot topics in copulas with a special focus on model selection and
goodness-of-fit testing
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