Abstract:We define the quantile set of order α ∈ [1/2, 1) associated to a law P on R d to be the collection of its directional quantiles seen from an observer O ∈ R d . Under minimal assumptions these star-shaped sets are closed surfaces, continuous in (O, α) and the collection of empirical quantile surfaces is uniformly consistent. Under mild assumptions -no density or symmetry is required for P -our uniform central limit theorem reveals the correlations between quantile points and a non asymptotic Gaussian approximat… Show more
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