Modelling the mean of a doubly stochastic Poisson process by functional data analysis

A new procedure for estimating the mean process of a doubly stochastic Poisson process is introduced. The proposed estimation is based on monotone piecewise cubic interpolation of the sample paths of the mean. In order to estimate the continuous time structure of the mean process functional principal component analysis is applied to its trajectories previously adapted to their functional form. A validation of the estimation method is presented by means of some simulations.