No. 1104

Title:

On parameter estimation based on the contact distance for certain superposed Neyman-Scott cluster fields

Author(s):

TANAKA, Ushio (The Institute of Statistical Mathematics)

Key words:

superposed Neyman-Scott cluster field; contact distance; nearest neighbor distance function; J-function; NND intensity analysis; unimodality; parameter estimation

Abstract:

    We consider parameter estimation of the superposed Neyman-Scott cluster field. This is typical of cluster point pattern model. We show that parameters of this model whose J-functions satisfy certain condition can be determined completely via an isotropic and non-homogeneous Poisson maximum likelihood analysis based on contact distance, which is defined as the shortest distance from the given location to the nearest point. The J-function is known as a useful tool assigning an index to spatial point pattern interaction. A sufficient condition for our method to hold is that the maximum log-likelihood function is unimodal. For such a cluster field, the proposed estimation procedure also enables us to generalize the number of the superposition.