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

• Published in: Statistics and computing Vol. 24; no. 1; pp. 91 - 100
• Main Authors: Mrkvicka, T, Muska, M, Kubecka, J
• Format: Journal Article
• Language: English
• Published: Boston Springer US 2014
• Subjects: Artificial Intelligence; Clusters; Ecological monitoring; Fish; Mathematical analysis; Mathematical models; Mathematics and Statistics; Probability and Statistics in Computer Science; Regression; Spatial distribution; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Modified; Bayesian method; function; Composite likelihood; Minimum contrast method; Neyman-Scott point process; Clustering; Inhomogeneous point process; Inhomogeneous cluster centers
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-012-9355-3

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.