Improving Upon the Marginal Empirical Distribution Function When the Copula is Known

Superefficient Estimation of the Marginals by Exploiting Knowledge on the Copula

“…The study of efficient estimation for semiparametric copula models originated in Klaassen and Wellner (1997), which focused on efficient estimation of the copula parameter and noted that exploiting the knowledge on the copula may help to improve on the marginal empirical distribution functions. Following the setup in Klaassen and Wellner (1997), Chen, Fan, and Tsyrennikov (2006), Van den Akker (2007, Chapter 5), and Segers, Van den Akker, and Werker (2010) provide efficient estimators of the marginals, incorporating the information the copula provides, with the standard rate of convergence n −1/2 and a limiting distribution that has less spread than the limiting distribution of the empirical distribution functions.…”