A note on estimation of the global intensity of a cyclic poisson process in the presence of linear trend

Abstract

ABSTRACT. We construct and investigate a consistent kernel-type non parametric estimator of the global intensity of a cyclic Poisson process in the presence of linear trend. 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. The asymptotic bias and variance of the proposed estimator are computed. Bias reductionof the estimator is also proposed. 1991 Mathematics Subject Classification: 60G55, 62GO5, 62G20. Keywords and Phrases: cyclic Poisson process, global intensity, linear trend, nonparametric estimation, consistency, bias, variance.