ESTIMATING THE INTENSITY IN THE FORM OF A POWER FUNCTION OF AN INHOMOGENEOUS POISSON PROCESS

An estimator of the intensity in the form of a power function of an inhomogeneous Poisson process is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance and the mean- squared error of the proposed estimator are computed. Asymptotic normality of the estimator is also established