Consistency of a Kernel-Type Estimator of the Intensity of the Cyclic Poisson Process With the Linear Trend

Abstract

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 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.