An Invitation to Multivariate Quantiles Arising from Optimal Transport Theory

While a variety of new concepts and methods arised from Optimal Transport theory recently in the literature, they are somewhat theoretical for empirical researchers, including statisticians and econometricians. This tutorial paper aims at elaborating on one of these new concepts and methods, namely multivariate quantile functions, in order to invite empirical researchers to take a closer look at this new concept to apply to their empirical works, such as multivariate quantile regression.