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Estimation for the Distribution of Two-dimensional Discrete Scan Statistics

Author

Listed:
  • G. Haiman

    (Université de Lille 1
    LSTA Université Paris 6)

  • C. Preda

    (Faculté de Médecine Université de Lille 2)

Abstract

This paper concerns the application of the method introduced in (Haiman, Extremes, 3:349–361, 2000) to estimate the distribution of two-dimensional discrete scan statistics. This method makes it possible to establish sharp bounds for the estimation errors. The method involves the estimation by simulation of the distribution of scan statistics for the particular rectangle sets of size 2×2, 2×3, 3×3, where the unit is the (m 1×m 2) dimension of the rectangular scanning window, m 1, m 2 ∈ℕ. We perform several numerical applications and compare our results with results obtained by other authors.

Suggested Citation

  • G. Haiman & C. Preda, 2006. "Estimation for the Distribution of Two-dimensional Discrete Scan Statistics," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 373-382, September.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:3:d:10.1007_s11009-006-9752-1
    DOI: 10.1007/s11009-006-9752-1
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    References listed on IDEAS

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    1. Chen, Jie & Glaz, Joseph, 1996. "Two-dimensional discrete scan statistics," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 59-68, December.
    2. Haiman, George, 1999. "First passage time for some stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 231-248, April.
    3. G. Haiman & C. Preda, 2002. "A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process," Methodology and Computing in Applied Probability, Springer, vol. 4(4), pages 393-407, December.
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    Cited by:

    1. Haiman, George & Preda, Cristian, 2013. "One dimensional scan statistics generated by some dependent stationary sequences," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1457-1463.
    2. Qianzhu Wu & Joseph Glaz, 2019. "Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 295-314, March.

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