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; I Wayan Mangku; Hadi Sumarno

doi:10.9734/BJAST/2015/17391

Research Article Open access CC BY 4.0

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, I Wayan Mangku, Hadi Sumarno

Current Journal of Applied Science and Technology · pp. 383–387 · Published 26 May 2015

10.9734/BJAST/2015/17391

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].

Poisson process periodic intensity function power function trend strong consistency complete convergence.

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Ikhsan Maulidi, I Wayan Mangku, Hadi Sumarno (2015). 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. Current Journal of Applied Science and Technology , 383–387. https://doi.org/10.9734/BJAST/2015/17391

Affiliations

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

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