# Adaptive Laguerre density estimation for mixed Poisson models

Abstract : In this paper, we consider the observation of $n$ i.i.d. mixed Poisson processes with random intensity having an unknown density $f$ on ${\mathbb R}^+$. For fixed observation time $T$, we propose a nonparametric adaptive strategy to estimate $f$. We use an appropriate Laguerre basis to build adaptive projection estimators. Non-asymptotic upper bounds of the ${\mathbb L}^2$-integrated risk are obtained and a lower bound is provided, which proves the optimality of the estimator. For large $T$, the variance of the previous method increases, therefore we propose another adaptive strategy. The procedures are illustrated on simulated data.
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Journal articles
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Cited literature [20 references]

https://hal.archives-ouvertes.fr/hal-00848158
Contributor : Fabienne Comte <>
Submitted on : Thursday, March 13, 2014 - 1:35:48 PM
Last modification on : Friday, September 20, 2019 - 4:34:03 PM
Long-term archiving on: Friday, June 13, 2014 - 11:20:26 AM

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### Citation

Fabienne Comte, Valentine Genon-Catalot. Adaptive Laguerre density estimation for mixed Poisson models. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2015, 9, pp.1112-1148. ⟨10.1214/15-EJS1028⟩. ⟨hal-00848158v2⟩

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