  Quantile regression, the prediction of conditional quantiles, finds
applications in various fields. Often, some or all of the variables are
discrete. The authors propose two new quantile regression approaches to handle
such mixed discrete-continuous data. Both of them generalize the continuous
D-vine quantile regression, where the dependence between the response and the
covariates is modeled by a parametric D-vine. D-vine quantile regression
provides very flexible models, that enable accurate and fast predictions.
Moreover, it automatically takes care of major issues of classical quantile
regression, such as quantile crossing and interactions between the covariates.
The first approach keeps the parametric estimation of the D-vines, but modifies
the formulas to account for the discreteness. The second approach estimates the
D-vine using continuous convolution to make the discrete variables continuous
and then estimates the D-vine nonparametrically. A simulation study is
presented examining for which scenarios the discrete-continuous D-vine quantile
regression can provide superior prediction abilities. Lastly, the functionality
of the two introduced methods is demonstrated by a real-world example
predicting the number of bike rentals.
