Estimation de quantiles géométriques conditionnels et non conditionnels

Chaouch, Mohamed; Gannoun, Ali; Saracco, Jérôme

Journal de la société française de statistique, Tome 150 (2009) no. 2, pp. 1-27.

L’absence d’un critère pour ordonner les observations représente un obstacle pour étendre la définition classique des quantiles univariés au cas multidimensionnel. Dans le cadre d’études biomédicales ou industrielles, par exemple, on cherche souvent à déterminer le quantile d’un vecteur aléatoire conditionnellement à un autre. Plusieurs définitions des quantiles (conditionnels) multivariés, ne reposant pas sur une relation d’ordre, ont été proposées dans la littérature statistique. Dans cet article, nous nous focalisons sur la notion de quantile géométrique et de quantile géométrique conditionnel, fondée sur la minimisation d’une fonction de perte.

Lack of objective basis for ordering multivariate observations is a major problem in extending the notion of quantiles in a multidimensional setting. Conditional quantiles are required in various biomedical or industrial problems. Numerous alternative definitions of (conditional) quantile for multidimensional variables, have been proposed in statistical literature. In this article, we focus on the notion of geometric quantile and conditional geometric quantile, based on the minimization of a loss function.

Classification : 62G05, 62H11, 62G20
Mot clés : algorithmes de calcul, estimateur à noyau, contours, quantile géométrique, quantile géométrique conditionnel, Transformation-Retransformation
Keywords: algorithm, geometric quantile, conditional geometric quantile, kernel estimator, contour plot, tranformation-retransformation estimate

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