A procedure relying on linear programming techniques is developed to compute (regression) quantile regions that have been defined recently. In the location case, this procedure allows for computing halfspace depth regions even beyond dimension two. The corresponding algorithm is described in...

This article defines a meaningful concept of elliptical location quantile with the aid of quantile regression, discusses its basic properties, and suggests its extension to a general regression framework through a locally constant nonparametric approach.

We consider asymptotic inference for the concentration of directional data. More precisely, wepropose tests for concentration (i) in the low-dimensional case where the sample size n goes to infinity andthe dimension p remains fixed, and (ii) in the high-dimensional case where both n and p become...

In this paper, we use quantization to construct a nonparametric estimator of conditionalquantiles of a scalar response Y given a d-dimensional vector of covariates X. First we focuson the population level and show how optimal quantization of X, which consists in discretizingX by projecting it on...