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Multiple-output quantile regression

par Hallin, Marc ;Šiman, Miroslav
Référence Handbook of Quantile Regression, CRC Press, page (185-207)
Publication Publié, 2017-01

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Résumé :

Quantile regression is about estimating the quantiles of some d-dimensional response Y conditional on the values x ∈ R p of some covariates X. The problem is well understood when d = 1 (single-output case, where Y is used instead of Y ): for a (conditional) probability 186distribution P Y = P X = x Y on R, with distribution function F = F X = x, the (conditional on X = x) quantile of order τ of Y is q τ (x) : = inf {y : F (y) ≥ τ}, τ ∈ [0, 1].