Estimating the intensity of a cyclic Poisson process in the presence of additive and multiplicative linear trend

Abstract

In this paper we survey some results on estimation of the intensity function of a cyclic Poisson process in the presence of additive and multiplicative linear trend. We do not assume any parametric form for the cyclic component of the intensity function, except that it is periodic. Moreover, we consider the case when there is only a single realization of the Poisson process is observed in a bounded interval. The considered estimators are weakly and strongly consistent when the size of the observation interval indefinitely expands. Asymptotic approximations to the bias and variance of those estimators are presented.