Single-index copulas

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Abstract

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.

AMS subject classifications

62F12
62G05

Keywords

Conditional copulas
Conditional Kendall’s tau
Kernel smoothing
Single-index models

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