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 Rd given covariates Z=z, taking values in Rk, is a map u -- QY|Z(u,z), which is monotone, in the sense of being a...

We propose new concepts of statistical depth, multivariate quantiles, vector quantiles and ranks, ranks, and signs, based on canonical transportation maps between a distribution of interest on Rd and a reference distribution on the d-dimensional unit ball. The new depth concept, called...

This note introduces a maximum likelihood estimator of the value of job amenities and labor productivity in a single matching market based on the observation of equilibrium matches and wages. The estimation procedure simultaneously fits both the matching patterns and the wage curve. Our...

In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory species the matching affinity and determines the optimal joint distribution. In contrast, we study the inverse...