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Mean Square Error Convergence of Kernel Type Estimator of the Intensity Function for Periodic Poisson Process.

Authors :
Rachmawati, Ro’fah Nur
Budiharto, Widodo
Source :
Procedia Engineering; Dec2012, Vol. 50, p474-485, 12p
Publication Year :
2012

Abstract

Abstract: In this paper, we construct the estimation for periodic component of the intensity function of a periodic Poisson process in the presence of power function trend with uniform kernel function. It is considered the worst case where there is only available a single realization of Poisson process having intensity which consist of a periodic component and a power function trend, observed in interval [0,n]. It is assumed that the period of periodic component is known and the slope of the power function trend is unknown. It has been formulated the estimator and the proof of convergence of the bias, variance and mean square error of the estimator. The proofs and the simulations produce the estimator that we construct is asymptotically unbiased estimator and mean square error of the estimator converge to zero while n is large. [Copyright &y& Elsevier]

Details

Language :
English
ISSN :
18777058
Volume :
50
Database :
Supplemental Index
Journal :
Procedia Engineering
Publication Type :
Academic Journal
Accession number :
82906391
Full Text :
https://doi.org/10.1016/j.proeng.2012.10.053