On Parameter Estimation by Aggregated Poisson Observations - Accrachi, Elhadji Ousseynouu; Aidara, Cherif Ahmat Tidiane; Dabye, Ali S. (Armenian Journal of Mathematics, 2022)
We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.