CONSISTENCY OF A KERNEL-TYPE ESTIMATOR OF THE INTENSITY OF THE CYCLIC POISSON PROCESS WITH THE LINEAR TREND

I Wayan Mangku (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor)
Siswadi - (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor)
Retno Budiarti (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor)

Journal of the Indonesian Mathematical Society
Volume 15 Number 1 (April 2009)

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 in definitely expands.DOI : http://dx.doi.org/10.22342/jims.15.1.42.37-48