A note on minimum distance estimation of copula densities

This paper introduces a minimum L, distance estimate for parametric copula densities. It is shown that the expected L, error of the estimate is within a given constant multiple of the best possible error plus an additive remainder term which is small under mild assumptions. The proof is based on an oracle inequality and a maximal inequality for the empirical copula process indexed by sets. (c) 2005 Elsevier B.V. All rights reserved.