Estimation des quantiles conditionnels par quantification optimale : nouveaux résultats

Abstract : We construct a nonparametric estimator of conditional quantiles of Y given X using optimal quantization. Conditional quantiles are particularly of interest when it is felt that conditonal mean is not representative of the impact of the covariable X on the dependent variable Y . Optimal quantization in L p -norm is a discretizing method used since the fifties in engineering. We use it to find the best approximation of X by a discrete version with support of size N . The aim of this work is to apply optimal quantization to conditional quantile estima-tion. We study the convergence of the approximation defined above (N → ∞) and of the resulting estimator (n → ∞). It was implemented in R in order to evaluate its numerical behavior and realize a simulation study. We then compare it with existing methods.
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Isabelle Charlier, Davy Paindaveine, Jérôme Saracco. Estimation des quantiles conditionnels par quantification optimale : nouveaux résultats. 46èmes Journées de Statistique, Jun 2014, Rennes, France. ⟨hal-01109003⟩

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