Some Ideas on Regularized Copula Estimation

Göran Kauermann (Ludwig-Maximilians-Universtät München)
Monday, January 23, 2012 - 2:15pm
Spandauer Strasse 1, Room 23

Regularized or penalized estimation, respectively, has become a powerful estimation technique in the last decades. The idea of penalized spline is a central element in regularized estimation and has been applied in numerous fields as the survey article by Ruppert, Wand & Carroll (Electronic Journal of Statistics, 2009) demonstrates. We pick up the idea of penalized estimation and apply it to the field of non- or semi-parametric copula estimation. We present three different ideas how smooth, penalized estimation can be employed to estimate copula densities. First, a so called sparse grid is used which allows for semi-parametric estimation in higher dimensions. Secondly, a Bayes and empirical Bayes estimation of mixed Archimedean copulas is presented. And third, a pair copula estimation with penalized Bernstein polynomials is suggested.