JSM 2005 Online Program

Abstract #302974

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Activity Number:	270
Type:	Contributed
Date/Time:	Tuesday, August 9, 2005 : 10:30 AM to 12:20 PM
Sponsor:	General Methodology
Abstract - #302974
Title:	Assessing Isotropy for Spatial Point Patterns
Author(s):	Michael Sherman*+
Companies:	Texas A&M University
Address:	Dept of Statistics, College Station, TX, 77843, United States
Keywords:	anisotropy ; spatial data ; subsampling
Abstract:	Spatial point process models are useful tools to model irregularly scattered point patterns frequently encountered in biological, ecological, and epidemiological studies. Examples include locations of biological cells in a tissue, of trees in a forest, or of leukemia patients in a state. A spatial point process is stationary if its distribution is invariant under translations. Further, it is said to be isotropic if its distribution is invariant under rotations about the origin. Otherwise, it is said to be anisotropic. The assumption of isotropy often is made in practice due to simpler interpretation and ease of analysis. In many situations, however, it is of great interest to assess isotropy and to subsequently perform a thorough directional analysis if the assumption of isotropy is untenable. We propose a formal nonparametric approach to test for isotropy based on the asymptotic joint normality of the sample second-order intensity function. We derive a consistent subsampling estimator for the asymptotic covariance matrix of the sample second-order intensity function and use this to construct a test statistic with a known limiting distribution.

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