15h30 - 15h55
A New, Exact, Distribution-Function-Based Goodness-of-Fit Test for Copulas
A common problem of many copula goodness-of-fit tests is that they may have little power in finite settings. The purpose of this paper is to address this issue. The notion of regularized test discussed by Diouf and Dufour (2008) will be used to design a new, distribution-function-based goodness-of-fit test for copulas. The properties of this test will be explored, and numerically intensive methods will be proposed for the computation of their p-value (Genest and Rémillard, 2008). In addition, the exact test will be derived using techniques described in Dufour (1989, 1990), Dufour and Kiviet (1996, 1998), and Dufour et al. (1998). A power study will be conducted to determine whether the proposed test has the desired finite-sample properties. The use of the test will be illustrated with financial data.
15h55 - 16h20
Estimation bayésienne de fonctions par la méthode du tamis
Dans l'exposé, nous verrons la méthode du tamis pour l'estimation de fonctions contraintes. Cette approche requiert la construction de sous-espaces d'approximation pour la fonction d'intérêt, le choix de lois a priori et la génération d'algorithmes efficaces pour l'approximation de l'estimateur de Bayes selon la fonction de perte choisie (moyenne a posteriori, map, etc.). Ces algorithmes sont générés en utilisant les méthodes Monte Carlo par chaînes de Markov. Des exemples seront présentés.
16h20 - 16h45
Mixtures of Empirical Copulas and Weighted Coefficients of Correlation
Ranks can be used to infer on the dependence structure of data without modelling its identically distributed margins. If data comes from sources that produce different margins, ranks cannot be calculated on the whole sample. Think for instance of observational data with categorical confounding variables, or of data calculated using different scales or indices on every populations. We construct mixtures of empirical copulas and weighted coefficients of correlation to analyze such data. The consistency of the estimates and their asymptotic distributions are derived for scalar weights. We also consider the case where data-based weights detect adaptively the similarities between the copulas underlying each population to compromise between bias and variance. Simulations and a case study are presented to explore the finite sample behaviour of these proposed methods.
16h45 - 17h10
Nonparametric Inference Techniques for Pair-Copula Constructions
Pair-copula constructions offer great flexibility in modeling multiple dependencies. For inference purposes, however, pair-copulas are often assumed to depend only indirectly on the conditioning variables. In this talk, I will show how this assumption can be circumvented using nonparametric smoothing techniques. Optimization and model selection issues will also be discussed.