Prediction via the Quantile-Copula Conditional Density Estimator

To make a prediction of a response variable from an explanatory one which takes into account features such as multimodality, a nonparametric approach based on an estimate of the conditional density is advocated and considered. In particular, we build point and interval predictors based on the quantile-copula estimator of the conditional density by Faugeras (2009). The consistency of these predictors is proved through a uniform consistency result of the conditional density estimator. Eventually, the practical implementation of these predictors is discussed. A simulation on a real data set illustrates the proposed methods.