Strong Consistency of a Kernel-type Estimator for the Intensity Obtained as the Product of a Periodic Function with the Power Function Trend of a Non-homogeneous Poisson Process
Ikhsan Maulidi *
Departement of Mathematics, Bogor Agricultural University, Jalan Meranti, Kampus IPB Dramaga Bogor 16680, Indonesia
I Wayan Mangku
Departement of Mathematics, Bogor Agricultural University, Jalan Meranti, Kampus IPB Dramaga Bogor 16680, Indonesia
Hadi Sumarno
Departement of Mathematics, Bogor Agricultural University, Jalan Meranti, Kampus IPB Dramaga Bogor 16680, Indonesia
*Author to whom correspondence should be addressed.
Abstract
In [1], a kernel-type estimator for the intensity obtained as the product of a periodic function with the power function trend of a non-homogeneous Poisson process has been formulated. In addition, asymptotic approximations to the bias, variance and mean squared error of this estimator have been established. In this paper, we construct a proof of strong consistency of the estimator proposed in [1].
Keywords: Poisson process, periodic intensity function, power function trend, strong consistency, complete convergence.