An application of directional quantiles to economic data with a multivariate response

Quantile regression represents a popular and useful methodology for modeling quantiles of a response variable based on one or more independent variables. Directional quantiles represent an available extension to the linear regression model with a multivariate response. However, we are not aware of any application of directional quantiles to real data in the literature. An illustration of directional quantiles to an economic dataset is presented in this paper, particularly a modeling of a two-dimensional response in the classical Engel's dataset on household consumption from the 19th century. The results reveal the directional quantiles to yield meaningful results. They order individual observations according to their depth, i.e. from the most central to the most outlying. We compare their result with those of a (more standard) outlier detection. On the whole, we perceive directional quantiles as a potentially useful tool for the analysis of data, if accompanied by a thorough analysis by standard tools.