MULTIVARIATE DENSITY ESTIMATION UNDER SUP-NORM LOSS: ORACLE APPROACH, ADAPTATION AND INDEPENDENCE STRUCTURE - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annals of Statistics Année : 2013

MULTIVARIATE DENSITY ESTIMATION UNDER SUP-NORM LOSS: ORACLE APPROACH, ADAPTATION AND INDEPENDENCE STRUCTURE

Résumé

This paper deals with the density estimation on R d under sup-norm loss. We provide a fully data-driven estimation procedure and establish for it a so-called sup-norm oracle inequality. The proposed estimator allows us to take into account not only approximation properties of the underlying density, but eventual independence structure as well. Our results contain, as a particular case, the complete solution of the bandwidth selection problem in the multi-variate density model. Usefulness of the developed approach is illustrated by application to adaptive estimation over anisotropic Nikolskii classes.
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Dates et versions

hal-01265250 , version 1 (02-02-2016)

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Oleg Lepski. MULTIVARIATE DENSITY ESTIMATION UNDER SUP-NORM LOSS: ORACLE APPROACH, ADAPTATION AND INDEPENDENCE STRUCTURE. Annals of Statistics, 2013, 41 (2), pp.1005-1034. ⟨10.1214/13-AOS1109⟩. ⟨hal-01265250⟩
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