Abstract
Empirical copula (EC) is a rank-based method for estimating the dependence structure of a random vector, which is convenient when someone wants to estimate non-parametrically the whole distribution of the random vector in two separated stages: rst the margins and then the dependence structure fully represented by a copula. The discrete nature of an EC can be successively smoothed using Bernstein polynomials approximation to obtain di fferentiable estimate of underlying copula or its density.
In practice, however, some components of some observations are often missing. In this case the marginal distributions of individual vector components can be estimated without any changes using all available information, whilst the second step is not so straightforward.
One can employ only complete observations to capture the dependence but then the mapping of estimated copula on individual marginal quantiles is not reflected appropriately. In the article the author suggests to generalize the classical EC to be applicable also on incomplete observations and further shows that Bernstein approximation based on this generalized EC is only slightly modi ed and all its important attributes remain unchanged.