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Title of Journal: Ann Inst Stat Math

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Abbravation: Annals of the Institute of Statistical Mathematics

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Springer-Verlag

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10.1002/div.2175

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1572-9052

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Estimating the intensity of a cyclic Poisson proce

Authors: Roelof Helmers I Wayan Mangku
Publish Date: 2007/11/07
Volume: 61, Issue: 3, Pages: 599-628
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Abstract

We construct and investigate a consistent kerneltype 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 meansquared 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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