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

I Wayan Mangku; Siswadi -; Retno Budiarti

doi:10.22342/jims.15.1.42.37-48

I Wayan Mangku ⁽¹⁾ , Siswadi - ⁽²⁾ , Retno Budiarti ⁽³⁾

(1) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor, Indonesia,

(2) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor, Indonesia,

(3) Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor, Indonesia

https://doi.org/10.22342/jims.15.1.42.37-48

Issue
Volume 15 Number 1 (April 2009)

Submitted
April 29, 2012

Accepted
May 7, 2012

Published
May 7, 2012

Keywords:

cyclic Poisson process, intensity function, linear trend, nonparametric estima- tion, consistency

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Abstract

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

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Authors

I Wayan Mangku

Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor

penulis@jims-a.org (Primary Contact)

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

Mangku, I. W., -, S., & Budiarti, R. (2012). CONSISTENCY OF A KERNEL-TYPE ESTIMATOR OF THE INTENSITY OF THE CYCLIC POISSON PROCESS WITH THE LINEAR TREND. Journal of the Indonesian Mathematical Society, 15(1), 37–48. https://doi.org/10.22342/jims.15.1.42.37-48