WinBUGS – A Bayesian modelling framework: Concepts, structure, and extensibility
Statistics and Computing
An Introduction to Copulas (Springer Series in Statistics)
An Introduction to Copulas (Springer Series in Statistics)
Generalized Additive Models (Texts in Statistical Science)
Generalized Additive Models (Texts in Statistical Science)
Archimedean copula estimation using Bayesian splines smoothing techniques
Computational Statistics & Data Analysis
Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
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This paper proposes finite mixtures of different Archimedean copula families as a flexible tool for modelling the dependence structure in multivariate data. A novel approach to estimating the parameters in this mixture model is presented by maximizing the penalized marginal likelihood via iterative quadratic programming. The motivation for the penalized marginal likelihood stems from an underlying Bayesian model that imposes a prior distribution on the parameter of each Archimedean copula family. An approximative marginal likelihood is obtained by a classical quadrature discretization of the integral w.r.t. each family-specific prior distribution, thus yielding a finite mixture model. Family-specific smoothness penalties are added and the penalized marginal likelihood is maximized using an iterative quadratic programming routine. For comparison purposes, we also present a fully Bayesian approach via simulation-based posterior computation. The performance of the novel estimation approach is evaluated by simulations and two examples involving the modelling of the interdependence of exchange rates and of wind speed measurements, respectively. For these examples, penalized marginal likelihood estimates are compared to the corresponding Bayesian estimates.