BANDWIDTH SELECTION IN KERNEL DENSITY ESTIMATION: ORACLE INEQUALITIES AND ADAPTIVE MINIMAX OPTIMALITY - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annals of Statistics Année : 2011

BANDWIDTH SELECTION IN KERNEL DENSITY ESTIMATION: ORACLE INEQUALITIES AND ADAPTIVE MINIMAX OPTIMALITY

Résumé

We address the problem of density estimation with L s-loss by selection of kernel estimators. We develop a selection procedure and derive corresponding L s-risk oracle inequalities. It is shown that the proposed selection rule leads to the estimator being minimax adaptive over a scale of the anisotropic Nikol'skii classes. The main technical tools used in our derivations are uniform bounds on the L s-norms of empirical processes developed recently by Goldenshluger and Lepski [Ann. Probab. (2011), to appear].
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Dates et versions

hal-01265258 , version 1 (02-02-2016)

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Alexander Goldenshluger, Oleg Lepski. BANDWIDTH SELECTION IN KERNEL DENSITY ESTIMATION: ORACLE INEQUALITIES AND ADAPTIVE MINIMAX OPTIMALITY. Annals of Statistics, 2011, 39 (3), pp.1608-1632. ⟨10.1214/11-AOS883⟩. ⟨hal-01265258⟩
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