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 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,ranks and signs, based on canonical transportation maps between a distributionof interest on IRd and a reference distribution on the d-dimensionalunit ball. The new depth concept, called Monge-Kantorovich depth, specializesto...

This paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions, also known as the quantile crossing problem. The method consists in sorting or monotone rearranging the original estimated non-monotone curve...

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

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...

Suppose that a target function f0 : Rd - R is monotonic, namely weakly increasing, and an original estimate f of this target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates f. We show that these estimates can always...