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Pré-Publication, Document De Travail Année : 2011

Density estimation for nonnegative random variables

Fabienne Comte
Valentine Genon-Catalot
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Résumé

We propose a new type of non parametric density estimators fitted to 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 value $m^{-1/2}$ plays the role of the bandwidth. We study the pointwise Mean Square Error and a weighted global Mean Integrated Square Error and propose adaptive estimators for both local and global points of view. The risks of the adaptive estimators satisfy oracle inequalities. A noteworthy result is that the adaptive rates are in correspondence with the smoothness properties of the unknown density as a function on $(0,+\infty)$. Pointwise adaptive estimators are illustrated on simulated data.
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Dates et versions

hal-00560104 , version 1 (27-01-2011)

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  • HAL Id : hal-00560104 , version 1

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Fabienne Comte, Valentine Genon-Catalot. Density estimation for nonnegative random variables. 2011. ⟨hal-00560104⟩
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