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A Robust Heuristic Estimator for the Period of a Poisson Intensity Function

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  • Mark Bebbington

    (Massey University)

  • Ričardas Zitikis

    (University of Western Ontario)

Abstract

While there are a number of methods for estimating the intensity of a cyclic point process, these assume prior estimation of the period itself. The standard method for the latter is the “periodogram,” or spectral analysis, approach. This is a parametric method which is sensitive to the form, in particular the number of peaks per cycle, of the intensity. We construct a family of nonparametric estimators for the period of a cyclic Poisson process, with the object of robustness against the form of the intensity. These are tested, along with the standard periodogram estimate and an earlier nonparametric estimator, on simulated data from a range of intensity functions. While the nonparametric estimators presently lack the well-developed asymptotic and statistical properties of the periodogram, the best of them is almost as accurate as the periodogram for the unimodal intensity cycles on which the latter is based. Whereas the periodogram cannot handle multimodal cycles at all, the better nonparametric estimators are reasonably accurate, and sometimes err by estimating multiples of the period rather than divisors, errors that are arguably less damaging. We conclude with some remarks concerning the derivation of asymptotic properties for our nonparametric estimator.

Suggested Citation

  • Mark Bebbington & Ričardas Zitikis, 2004. "A Robust Heuristic Estimator for the Period of a Poisson Intensity Function," Methodology and Computing in Applied Probability, Springer, vol. 6(4), pages 441-462, December.
  • Handle: RePEc:spr:metcap:v:6:y:2004:i:4:d:10.1023_b:mcap.0000045090.84875.22
    DOI: 10.1023/B:MCAP.0000045090.84875.22
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    References listed on IDEAS

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    1. Linda Green & Peter Kolesar, 1991. "The Pointwise Stationary Approximation for Queues with Nonstationary Arrivals," Management Science, INFORMS, vol. 37(1), pages 84-97, 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.
    3. Mary A. Johnson & Sanghoon Lee & James R. Wilson, 1994. "Experimental Evaluation of a Procedure for Estimating Nonhomogeneous Poisson Processes Having Cyclic Behavior," INFORMS Journal on Computing, INFORMS, vol. 6(4), pages 356-368, November.
    4. 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.
    5. Kuhl, Michael E. & Wilson, James R., 2001. "Modeling and simulating Poisson processes having trends or nontrigonometric cyclic effects," European Journal of Operational Research, Elsevier, vol. 133(3), pages 566-582, September.
    6. Edward P. C. Kao & Sheng-Lin Chang, 1988. "Modeling Time-Dependent Arrivals to Service Systems: A Case in Using a Piecewise-Polynomial Rate Function in a Nonhomogeneous Poisson Process," Management Science, INFORMS, vol. 34(11), pages 1367-1379, November.
    7. Chukova, Stefanka & Dimitrov, Boyan & Garrido, José, 1993. "Renewal and nonhomogeneous Poisson processes generated by distributions with periodic failure rate," Statistics & Probability Letters, Elsevier, vol. 17(1), pages 19-25, May.
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    1. 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.

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