ANALYSIS OF SPATIAL POINT PATTERNS BY KERNEL IDENTIFICATION

Document Type: Regular Paper

Authors

Department of Statistics, Shahid Beheshti University, Evin, Tehran, I. R. of Iran 19839

Abstract

In the analysis of spatial point patterns, complete spatial randomness (CSR) hypothesis,
which is a restriction of a homogenous Poisson process to study region A, operates as a dividing
hypothesis between “regular” and “aggregated” patterns. Meanwhile, many alternatives to CSR in
aggregated patterns are extensions of homogenous Poisson processes themselves. Therefore, when the
CSR hypothesis is rejected, results related to Poisson processes may be used to formulate plausible
alternatives to CSR. In this paper, we propose a new statistic for testing CSR and then by applying it in
conjunction with a notion of kernels of a point pattern, we determine the “parents” of a Poisson cluster
process when the CSR hypothesis is rejected and a Neyman-Scott process is assumed for the point
pattern under alternative hypothesis. We have made power studies for our test statistic by simulation, and
have also surveyed the performance of our method on a certain point pattern. Finally, the whole method
is carried on certain real life data.

Keywords