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An Estimation Method of the Pair Potential Function for Gibbs Point Processes on Spheres

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  • Jean‐Michel Billiot
  • Michel Goulard

Abstract

An estimation method for pairwise interaction potential of a stationary Gibbs point process is introduced by considering the case of observations located on a sphere. It is based both on Fourier decomposition of the potential and on minimum contrast estimation. It is defined when many independent realizations of the process are available. Consistency and asymptotic normality are proved for the resulting estimators. The method enables derivation of the choice of the potential function by embedded hypotheses testing. The method is applied to independent observations of root locations on internodes around stem of maize roots. The internodes are described as circles and we focus on the interaction function associated with the potential. Since a model with too many components seems to fail, we choose a sequential procedure based on embedded hypotheses testing to build a simpler model.

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  • Jean‐Michel Billiot & Michel Goulard, 2001. "An Estimation Method of the Pair Potential Function for Gibbs Point Processes on Spheres," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 185-203, March.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:1:p:185-203
    DOI: 10.1111/1467-9469.00231
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    Cited by:

    1. Gregori, P. & van Lieshout, M. N. M. & Mateu, J., 2004. "Mixture formulae for shot noise weighted point processes," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 311-320, May.

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