L2-CONVERGENCE OF A NEAREST NEIGHBOR ESTIMATOR OF THE INTENSITY FUNCTION OF A CYCLIC POISSON PROCES

Abstract

Abstract. We consider the problem of estimating the intensity func- tion of a cyclic Poisson process. We suppose that only a single realization of the cyclic Poisson process is observed within a bounded 'window', and our aim is to estimate consistently the intensity function at a given point. A nearest neighbor estimator of the intensity function is proposed, and we show that our estimator is L2-consistent, as the window expands.
AMS 2010 subject classifications: 62E20, 62G05, 62G20.
Key words and phrases: cyclic Poisson process, cyclic intensity function, nonparametric estimation, nearest neighbor estimator, period, consis- tency, L2-convergence.