We consider the problem of estimating the marginals in case there is knowledge on the copula. If the copula is smooth, it is known that it is possible to improve on the empirical distribution functions: optimal estimators still have rate of convergence n−1/2, but a smaller asymptotic variance. In this paper we show that smoothness assumptions on the copula are necessary: we construct both a (non-smooth) copula and, exploiting the information our copula provides, estimators of the marginals with rate of convergence log n/n.
|Place of Publication||Tilburg|
|Number of pages||8|
|Publication status||Published - 2010|
|Name||CentER Discussion Paper|
- estimation of marginals
- superefficient estimation