Beatriz Vaz do Melo Mendes
Robust Fits for Copula Models
We propose and compare two different methodologies for fitting copulas robustly. The first proposal consists in a robustification of the maximum likelihood method, where points previously identified as outliers by a high breakdown point covariance matrix estimator, are downweighted in a maximum likelihood optimization procedure. The second proposal obtains robust estimates by minimizing selected empirical copula based goodness of fit statistics.
We show through simulations that the proposed robust estimators are able to capture, under contaminations, the correct strength of dependence of the data and thus to correctly estimate the copula based dependence measures such as the tail dependence coefficient. The experiments considered several epsilon-contaminated copula models, for varying proportions epsilon of contaminating points. We also provide illustrations using real data.