Adaptive pointwise estimation of conditional density function

Abstract : In this paper we consider the problem of estimating $f$, the conditional density of $Y$ given $X$, by using an independent sample distributed as $(X,Y)$ in the multivariate setting. We consider the estimation of $f(x,.)$ where $x$ is a fixed point. We define two different procedures of estimation, the first one using kernel rules, the second one inspired from projection methods. Both adapted estimators are tuned by using the Goldenshluger and Lepski methodology. After deriving lower bounds, we show that these procedures satisfy oracle inequalities and are optimal from the minimax point of view on anisotropic Hölder balls. Furthermore, our results allow us to measure precisely the influence of $\mathrm{f}_X(x)$ on rates of convergence, where $\mathrm{f}_X$ is the density of $X$. Finally, some simulations illustrate the good behavior of our tuned estimates in practice.
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Article dans une revue
Annales de l'Institut Henri Poincaré, 2016, 52 (2), pp.939-980
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https://hal.archives-ouvertes.fr/hal-00922555
Contributeur : Vincent Rivoirard <>
Soumis le : vendredi 26 décembre 2014 - 13:52:38
Dernière modification le : jeudi 11 janvier 2018 - 06:12:21
Document(s) archivé(s) le : vendredi 27 mars 2015 - 12:05:34

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• HAL Id : hal-00922555, version 2
• ARXIV : 1312.7402

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Karine Bertin, Claire Lacour, Vincent Rivoirard. Adaptive pointwise estimation of conditional density function. Annales de l'Institut Henri Poincaré, 2016, 52 (2), pp.939-980. 〈hal-00922555v2〉

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