Adaptive Laguerre density estimation for mixed Poisson models

作者：Comte Fabienne^*; Genon Catalot Valentine

来源：Electronic Journal of Statistics, 2015, 9(1): 1113-1149.

DOI：10.1214/15-EJS1028

• Adaptive estimators
• inverse problem
• Laguerre basis
• nonparametric estimation
• poisson mixture

in Pus 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-2-integrated risk are obtained and a lower bound is provided, which proves the optimality of the estimator. For large F, the variance of the previous method increases, therefore we propose another adaptive strategy. The procedures are illustrated on simulated data.

• 出版日期2015