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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.