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...

Charlier, Paindaveine, and Saracco (2014) recently introduced a nonparametric estimatorof conditional quantiles based on optimal quantization, but almost exclusively focused onits theoretical properties. In this paper, (i) we discuss its practical implementation (byproposing in particular a...

This paper provides optimal testing procedures for the m-sample null hypothesis of Common Principal Components (CPC) under possibly non Gaussian and heterogenous elliptical densities. We first establish, under very mild assumptions that do not require finite moments of order four, the local...