Erwan Le Pennec

Copula

joint work with K. Tribouley and F. Autin

A $d$-dimensional copula is a distribution on $[0,1]p^d$ such that its marginals are uniforms on $[0,1]$ A theorem due to Sklar allows to express the law $H$ of a $d$-dimensional vector through the action of the unique copula $C$ on its marginals $F_i$ $$ H(x_1,\ldots,x_d) = C(F_1(x_1),\ldots,F_d(X_d)) $$ as soos as those marginals are continuous. We propose here an estimator of this copula $C$ or rather its density $$ c(u_1,\ldots,u_d) = \frac{h(F_1^{-1}(u_1),\ldots,F_d^{-1}(u_d))}{ f_1(F_1^{-1}(u_1))\cdots f_d(F_d^{-1}(u_d))}, $$ whose existence is supposed, by a wavelet thresholding method similar to the one used in density estimation.

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