Consistency Of A Kernel-Type Estimator Of The Intencity Of The Cyclic Poisson Process With The Linear Trend

Abstract

A consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process in the presence of linear trend is constructed and investigated. It is assumed that only a single realization of \he Poisson process is observed in a bounded window. We prove that the propoeed estimator is consistent when the size of the window indefinitely expands.