Statistical properties of a kernel-type estimator of the intensity function of a cyclic Poisson process

Abstract

We consider a kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process when the period is unknown. We assume that only a single realization of the Poisson process is observed in a bounded window which expands in time. We compute the asymptotic bias, variance, and the mean-squared error of the estimator when the window indefinitely expands. Author Keywords: Poisson process; Point process; Intensity function; Period; Nonparametric estimation; Consistency; Bias; Variance; Mean-squared error