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Nonparametric estimation of intensities of nonhomogeneous Poisson processes

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Abstract

The problem of nonparametric estimation of the intensity of a nonhomogeneous Poisson process is considered. A kernel estimator of the intensity is introduced with data driven bandwidth. The bandwidth is obtained from an L2 cross validation procedure. Results on almost sure convergence of the estimator are obtained, provided the number of observed realizations n tends to infinity. The limiting distribution of the estimator is presented for n→∞.

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  1. Agency for Safety of Aerospace Products, Gustav-Heinemann-Ufer 54, D-5000, Köln 51

    H. Schäbe

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  1. H. Schäbe
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Schäbe, H. Nonparametric estimation of intensities of nonhomogeneous Poisson processes. Statistical Papers 34, 113–131 (1993). https://doi.org/10.1007/BF02925534

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  • DOI: https://doi.org/10.1007/BF02925534

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