## Electronic Journal of Statistics

### 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.

#### Article information

Source
Electron. J. Statist. Volume 9, Number 1 (2015), 1113-1149.

Dates
First available in Project Euclid: 27 May 2015

https://projecteuclid.org/euclid.ejs/1432732306

Digital Object Identifier
doi:10.1214/15-EJS1028

Mathematical Reviews number (MathSciNet)
MR3352069

Zentralblatt MATH identifier
1328.62228

Subjects
Primary: 62G07: Density estimation
Secondary: 62C20: Minimax procedures

#### Citation

Comte, Fabienne; Genon-Catalot, Valentine. Adaptive Laguerre density estimation for mixed Poisson models. Electron. J. Statist. 9 (2015), no. 1, 1113--1149. doi:10.1214/15-EJS1028. https://projecteuclid.org/euclid.ejs/1432732306

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