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1 results

  • Maximum likelihood estimation for cooperative sequential adsorption

  • Part of
  • Mathew D. Penrose, Vadim Shcherbakov
  • Journal:
    Advances in Applied Probability / Volume 41 / Issue 4 / December 2009
    Published online by Cambridge University Press:
    01 July 2016, pp. 978-1001
    Print publication:
    December 2009
    • Article
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  • We consider a model for a time series of spatial locations, in which points are placed sequentially at random into an initially empty region of ℝd, and given the current configuration of points, the likelihood at location x for the next particle is proportional to a specified function βk of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters βk (assumed to be zero for k exceeding some fixed threshold) is consistent in the thermodynamic limit where the number of points grows in proportion to the size of the region.