Robust Fits for Copula Models

Abstract

In this paper we obtain robust estimators for copula parameters through the minimization of weighted goodness of¯t statistics. Di®erent weight functions emphasize di®erent regions on the unit square and are able to handle di®erent locations of model violation. The resulting W MDE estimators are compared to the classical maximum likelihood estimators MLE, and to their weighted version W MLE, an estimator obtained in two steps. The weights obtained in the¯rst step by the application of a high breakdown point scatter matrix estimator are used to identify atypical points. All estimators are compared in a comprehensive simulation study. For each ²-contaminated parametric copula family considered, we showed that there is a robust estimator improving over the MLE and able to capture the correct strength of dependence of the data, despite the contamination percentual and location, and the sample size.

Speech signal modeling using multivariate distributions

“…There are several estimation methods proposed for copula parameters [22,[35][36][37]. Among them, maximum likelihood (ML), inference functions for margins (IFM), and canonical maximum likelihood (CML) techniques are used more frequently than others [22].…”

Multivariate VaRs for operational risk capital computation: a vine structure approach

“…We use a pseudo maxi- 4 Other distributions have been tested but we only provide some results obtained using the Generalized Pareto Distribution in the fifth section mum likelihood method to estimate the copulas parameters (Mendes et al (2007), Weiss (2010) providing the value of the corresponding AIC (Akaike (1974)) in order to discriminate between different classes of copulas. We select our model following a triple statement:…”

On the Robustness of Goodness-of-Fit Tests for Copulas

“…To the best knowledge of the author, the only study that is concerned with the robustness of copula models is Mendes et al (2007) (recent papers by Kim et al (2007) and Fantazzini (2009a) focus on the 1 robustness of copula models to misspecified marginals; however, they do not consider contaminated data). In their work, Mendes et al (2007) derive robust estimators for the parameters of copulas and analyse their finite sample properties by means of a simulation study. The two strategies they employ to robustify the estimation of copula parameters include (1) the inclusion of weight functions in Minimum-Distance estimators and (2) the identification and exclusion of outliers.…”

“…While Mendes et al (2007) only use the DonohoStahel projection based estimator of multivariate location and scatter in their simulation study, we compare the Minimum Covariance Determinant estimator of Rousseeuw (1985), the Donoho-Stahel estimator, Rocke's constrained M-estimator, the S-estimator based on Tukey's biweight function and the orthogonalized Gnanadesikan-Kettenring estimator with each other regarding their ability to robustify the results of the copula GoF-tests. Fourth, this paper is the first to analyse the effects of mistakingly assuming a single parametric copula when the data actually stems from a mixture copula.…”

“…In a copula setting, the only study concerned with the robust estimation of copula parameters is due to Mendes et al (2007). In their work, only the Donoho-Stahel estimator is used for robustly estimating the location and scale of the multivariate data.…”