Nonparametric density estimation for mixed Poisson processes

Fabienne Comte (1) , Valentine Genon-Catalot (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

In this paper, we consider the observation of $n$ i.i.d. mixed Poisson processes with random intensity having an unknown density $f$ on ${\mathbb R}^+$. Depending on the observation time, we propose two nonparametric adaptive strategies to estimate $f$. We use an appropriate Laguerre basis to build adaptive projection estimators and also propose kernel estimators with adaptive bandwidths. Non-asymptotic bounds of the ${\mathbb L}^2$-integrated risk are obtained in each case. The procedures are illustrated on simulated data.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Fabienne Comte, Valentine Genon-Catalot. Nonparametric density estimation for mixed Poisson processes. 2013. ⟨hal-00848158v1⟩