Probit transformation for nonparametric kernel estimation of the copula density

Understand

Copula modelling has become ubiquitous in modern statistics.

• Here, the problem of nonparametrically estimating a copula density is addressed.
• Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable for the unit-square-supported copula densities, mainly because it is heavily affected by boundary bias issues.
• In addition, most common copulas admit unbounded densities, and kernel methods are not consistent in that case.