Single-index copulae

We introduce so-called “single-index copulae”. They are semi-parametric conditional copulae whose parameter is an unknown “link” function of a univariate index only. We provide estimates of this link function and of the finite dimensional unknown parameter. The asymptotic properties of the latter estimates are stated. Thanks to some properties of conditional Kendall’s tau, we illustrate our technical conditions with several usual copula families.