Convolution power kernels for density estimation - Archive ouverte HAL
Article Dans Une Revue Journal of Statistical Planning and Inference Année : 2012

Convolution power kernels for density estimation

Fabienne Comte
Valentine Genon-Catalot
  • Fonction : Auteur
  • PersonId : 836340

Résumé

We propose a new type of non-parametric density estimators fitted to random variables with lower or upper-bounded support. To illustrate the method, we focus on nonnegative random variables. The estimators are constructed using kernels which are densities of empirical means of m i.i.d. nonnegative random variables with expectation 1. The exponent m plays the role of the bandwidth. We study the pointwise mean square error and propose a pointwise adaptive estimator. The risk of the adaptive estimator satisfies an almost oracle inequality. A noteworthy result is that the adaptive rate is in correspondence with the smoothness properties of the unknown density as a function on (0,+∞). The adaptive estimators are illustrated on simulated data. We compare our approach with the classical kernel estimators.
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Dates et versions

hal-00681309 , version 1 (21-03-2012)

Identifiants

  • HAL Id : hal-00681309 , version 1

Citer

Fabienne Comte, Valentine Genon-Catalot. Convolution power kernels for density estimation. Journal of Statistical Planning and Inference, 2012, 142 (7), pp.1698-1715. ⟨hal-00681309⟩
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