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Uniform LAN condition of planar Gibbsian point processes and optimality of maximum likelihood estimators of soft-core potential functions
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  • Published: March 1992

Uniform LAN condition of planar Gibbsian point processes and optimality of maximum likelihood estimators of soft-core potential functions

  • Shigeru Mase1 

Probability Theory and Related Fields volume 92, pages 51–67 (1992)Cite this article

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Summary

A parametric model of planar point patterns in a bounded region is constructed using grand canonical Gibbsian point processes with soft-core potential functions. A simple and explicit condition that this model becomes a uniform locally asymptotic normal (ULAN) family will be given. From this result we can conclude that the maximum likelihood estimator of the potential function is asymptotically efficient for a wide class of loss functions.

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Authors and Affiliations

  1. Faculty of Integrated Arts and Sciences, Hiroshima University, Hiroshima, 730, Japan

    Shigeru Mase

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  1. Shigeru Mase
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Mase, S. Uniform LAN condition of planar Gibbsian point processes and optimality of maximum likelihood estimators of soft-core potential functions. Probab. Th. Rel. Fields 92, 51–67 (1992). https://doi.org/10.1007/BF01205236

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  • Received: 23 October 1989

  • Revised: 29 July 1991

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01205236

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Keywords

  • Stochastic Process
  • Probability Theory
  • Potential Function
  • Loss Function
  • Mathematical Biology
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