Multivariate quantiles and multiple-output regression quantiles: From L1 optimization to halfspace depth
نویسندگان
چکیده
منابع مشابه
Multivariate Quantiles and Multiple-output Regression Quantiles: from L1 Optimization to Halfspace Depth
A new multivariate concept of quantile, based on a directional version of Koenker and Bassett’s traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version, those quantiles can be computed efficiently via linear programming techniques. Consistency, Bahadur representation and asymptotic normality results are establ...
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In the multiple-output regression context, Hallin, Paindaveine and Šiman (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 Šiman (2010b) described a first elegan...
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Quantile regression is a wide spread regression technique which allows to model the entire conditional distribution of the response variable. A natural extension to the case of censored observations was introduced by Portnoy (2003) using a reweighting scheme based on the Kaplan-Meier estimator. We apply the same ideas on the depth quantiles defined in Rousseeuw and Hubert (1999). This leads to ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2010
ISSN: 0090-5364
DOI: 10.1214/09-aos723