Vine copula-based regression models

Vine copulas can also be used to construct flexible classes of regression models which can accommodate non linear non Gaussian dependence. This will include models for univariate and bivariate responses. For this the conditional distribution of the response given the covariates will be derived from a joint vine copula model of response and covariates. This provides a distribution regression model allowing for simple determination of conditional quantiles. The vine copula based regression models are constructed in such a way that the conditional density can be written explicitly without integration. This allows us also to develop a forward selection strategy to avoid overfitting. These approaches will be introduced and an application involving assessing risks in flight landings will be given.