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An empirical central limit theorem with applications to copulas under weak dependence |
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| Authors: | Paul Doukhan Jean-David Fermanian Gabriel Lang |
| Institution: | (1) ENSAE-CREST, J120, 3 Av. Pierre Larousse, 92245 Malakoff Cedex, France;(2) SAMOS, Université Paris 1, Centre Pierre Mendès, 90 ruede Tolbiac, 75634 Paris Cedex 13, France;(3) CREST, J320, 15 bd Gabriel Péri, 92245 Malakoff Cedex, France;(4) UMR, 518, MIA INRA AgroParisTech, AgroParisTech, 19 Avenue du Maine, 75732 Paris Cedex 15, France |
| Abstract: | We state a multidimensional Functional Central Limit Theorem for weakly dependent random vectors. We apply this result to copulas. We get the weak convergence of the empirical copula process and of its smoothed version. The finite dimensional convergence of smoothed copula densities is also proved. A new definition and the theoretical analysis of conditional copulas and their empirical counterparts are provided. |
| Keywords: | Copulas Multivariate FCLT Weak dependence |
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