Single-index copulas
Résumé
We introduce so-called single-index copulas. They are semi-parametric conditional copulas whose parameter is an unknown link function of a univariate index only. We propose 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.
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