Multivariate rank, quantile and regression via optimal transport

In this talk, I will introduce a novel Center-outward multivariate rank/quantile definition based on optimal transport theory, i.e. Monge-Kantorovich rank/quantile (Hallin et al. 2017), and review some other multivariate rank/quantile definitions. As an application of MK-quantile, we proposed a multivariate version composite quantile regression and demonstrates its theoretical property.