Mean-Square Convergence of Recursive Kernel Estimators of Non-Homogeneous Poisson Process Intensity Function and its Derivative

Abstract

The structure of the estimators is similar to the recursive kernel estimators of a density function and its derivative. The estimators have been constructed using a single realization of Poisson process on a fixed time interval. Mean-square convergence has been proved in a scheme of series. Simulation studies have been carried out to illustrate the convergence.