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Statistical properties of a kernel-type estimator of the intensity function of a cyclic Poisson process

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  • Helmers, Roelof
  • Mangku, I. Wayan
  • Zitikis, Ricardas

Abstract

We consider a kernel-type nonparametric estimator of the intensity function of a cyclic Poisson process when the period is unknown. We assume that only a single realization of the Poisson process is observed in a bounded window which expands in time. We compute the asymptotic bias, variance, and the mean-squared error of the estimator when the window indefinitely expands.

Suggested Citation

  • Helmers, Roelof & Mangku, I. Wayan & Zitikis, Ricardas, 2005. "Statistical properties of a kernel-type estimator of the intensity function of a cyclic Poisson process," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 1-23, January.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:1:p:1-23
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    References listed on IDEAS

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    1. Helmers, Roelof & Wayan Mangku, I. & Zitikis, Ricardas, 2003. "Consistent estimation of the intensity function of a cyclic Poisson process," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 19-39, January.
    2. Roelof Helmers & Ričardas Zitikis, 1999. "On Estimation of Poisson Intensity Functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 265-280, June.
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    Cited by:

    1. Nan Shao & Keh‐Shin Lii, 2011. "Modelling non‐homogeneous Poisson processes with almost periodic intensity functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 99-122, January.
    2. Roelof Helmers & I. Mangku, 2009. "Estimating the intensity of a cyclic Poisson process in the presence of linear trend," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 599-628, September.
    3. Eduard Belitser & Paulo Serra & Harry Van Zanten, 2013. "Estimating the Period of a Cyclic Non-Homogeneous Poisson Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 204-218, June.
    4. Roelof Helmers & I. Mangku, 2012. "Predicting a cyclic Poisson process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1261-1279, December.
    5. Roelof Helmers & Qiying Wang & Ričardas Zitikis, 2009. "Confidence regions for the intensity function of a cyclic Poisson process," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 21-36, February.
    6. José Miranda & Pedro Morettin, 2011. "Estimation of the intensity of non-homogeneous point processes via wavelets," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1221-1246, December.
    7. Grant, James A. & Leslie, David S. & Glazebrook, Kevin & Szechtman, Roberto & Letchford, Adam N., 2020. "Adaptive policies for perimeter surveillance problems," European Journal of Operational Research, Elsevier, vol. 283(1), pages 265-278.

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