Estimating The Intensity Obtained As The Product Of A Periodic Function With The Quadratic Trend Of A Non-Homogeneous Poisson Process

Abstract

A kernel-type nonparametric estimator of the intensity obtained as the product of a periodic function with the quadratic trend of a nonhomogeneous Poisson process is constructed and investigated. It is considered the case when there is only a single realization of the Poisson process is observed in a bounded interval. The proposed estimator is proved to be weakly and strongly consistent when the size of the interval indefinitely expands. The asymptotic bias, variance, and the mean-squared error of the proposed estimator are also computed.