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Computing multiple-output regression quantile regions from projection quantiles

par Paindaveine, Davy ;Siman, Miroslav
Référence Computational statistics, 27, page (29-49)
Publication Publié, 2012

Article révisé par les pairs

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Résumé :

In the multiple-output regression context, Hallin, Paindaveine and Siman (2010) introduced a powerful data-analytical tool based on regression quantile regions. However, the computation of these regions, that are obtained by considering in all directions an original concept of directional regression quantiles, is a very challenging problem. Paindaveine and Siman (2010b) described a first elegant solution relying on linear programming techniques. The present paper provides another solution based on the fact that the quantile regions can also be computed from a competing concept of projection regression quantiles, elaborated in Kong and Mizera (2008) and Paindaveine and Siman (2010a). As a by-product, this alternative solution further provides various characteristics useful for statistical inference. We describe in detail the algorithm solving the parametric programming problem involved, and illustrate the resulting procedure on simulated data. We show through simulations that the Matlab implementation of the algorithm proposed in this paper is faster than that from Paindaveine and Siman (2010b) in various cases.