Estimating the intensity of a cyclic Poisson process in the presence of linear trend |
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Authors: | Roelof Helmers I Wayan Mangku |
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Institution: | (1) Centre for Mathematics and Computer Science (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;(2) Department of Mathematics, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor, 16680, Indonesia |
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Abstract: | We construct and investigate a consistent kernel-type nonparametric estimator of the intensity function of a cyclic Poisson
process in the presence of linear trend. 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 indefinitely expands. The
asymptotic bias, variance, and the mean-squared error of the proposed estimator are also computed. A simulation study shows
that the first order asymptotic approximations to the bias and variance of the estimator are not accurate enough. Second order
terms for bias and variance were derived in order to be able to predict the numerical results in the simulation. Bias reduction
of our estimator is also proposed. |
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Keywords: | Cyclic Poisson process Intensity function Linear trend Nonparametric estimation Consistency Bias Variance Mean-squared error |
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