Empirical likelihood based confidence regions for functional of copulas

Abstract

In the present paper, we are mainly concerned with the statistical inference for the functional of nonparametric copula models satisfying linear constraints. The asymptotic properties of the obtained estimates and test statistics are given. Finally, a general notion of bootstrap for the proposed estimates and test statistics, constructed by exchangeably weighting sample, is presented, which is of its own interest. These results are proved under some standard structural conditions on some classes of functions and some mild conditions on the model, without assuming anything about the marginal distribution functions, except continuity. Our theoretical results and numerical examples by simulations demonstrate the merits of the proposed techniques.