Vector quantile regression: An optimal transport approach
向量分位数回归：最优传输方法
We propose a notion of conditional vector quantile function and a vector quantile regression. A conditional vector quantile function (CVQF) of a random vector $Y$, taking values in $\mathbb{R}^{d}$ given covariates $Z=z$, taking values in $\mathbb{R}^{k}$, is a map $u\longmapsto Q_{Y|Z}(u,z)$, which is monotone, in the sense of being a gradient of a convex function, and such that given that vector $U$ follows a reference non-atomic distribution $F_{U}$, for instance uniform…