Article

Statistics and Computing

, Volume 24, Issue 1, pp 91-100

Two step estimation for Neyman-Scott point process with inhomogeneous cluster centers

  • T. MrkvičkaAffiliated withDepartment of Applied Mathematics and Informatics, Faculty of Economics, University of South Bohemia Email author 
  • , M. MuškaAffiliated withBiology center of the AS CR, Institute of HydrobiologyFaculty of Science, University of South Bohemia
  • , J. KubečkaAffiliated withBiology center of the AS CR, Institute of HydrobiologyFaculty of Science, University of South Bohemia

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Abstract

This paper is concerned with parameter estimation for the Neyman-Scott point process with inhomogeneous cluster centers. Inhomogeneity depends on spatial covariates. The regression parameters are estimated at the first step using a Poisson likelihood score function. Three estimation procedures (minimum contrast method based on a modified K function, composite likelihood and Bayesian methods) are introduced for estimation of clustering parameters at the second step. The performance of the estimation methods are studied and compared via a simulation study. This work has been motivated and illustrated by ecological studies of fish spatial distribution in an inland reservoir.

Keywords

Bayesian method Composite likelihood Clustering Inhomogeneous cluster centers Inhomogeneous point process Minimum contrast method Modified K function Neyman-Scott point process