Convolution power kernels for density estimation

Abstract : 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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Article dans une revue
Journal of Statistical Planning and Inference, Elsevier, 2012, 142 (7), pp.1698-1715
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https://hal.archives-ouvertes.fr/hal-00681309
Contributeur : Fabienne Comte <>
Soumis le : mercredi 21 mars 2012 - 11:14:52
Dernière modification le : mardi 11 octobre 2016 - 11:57:25

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  • HAL Id : hal-00681309, version 1

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

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