Adaptive Laguerre density estimation for mixed Poisson models

In this paper, we consider the observation of n i.i.d. mixed Poisson processes with random intensity having an unknown density f on 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 L-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. March 13, 2014