Relative Density of the Random r-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association (Technical Report)

Details Relative Density of the Random r-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association (Technical Report) Relative Density of the Random r-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association (Technical Report)

2009-06-30

arxiv.org/abs/0906.5436v1

Mathematics

Statistics Theory

65 pages, 45 figures

Scientific paper

Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes. Different random graphs result from different definitions of the proximity region associated with each data point and different graph statistics can be employed for data reduction. The approach used in this article is based on a parameterized family of proximity maps determining an associated family of data-random digraphs. The relative arc density of the digraph is used as the summary statistic, providing an alternative to the domination number employed previously. An important advantage of the relative arc density is that, properly re-scaled, it is a U-statistic, facilitating analytic study of its asymptotic distribution using standard U-statistic central limit theory. The approach is illustrated with an application to the testing of spatial patterns of segregation and association. Knowledge of the asymptotic distribution allows evaluation of the Pitman and Hodges-Lehmann asymptotic efficacy, and selection of the proximity map parameter to optimize efficacy. Notice that the approach presented here also has the advantage of validity for data in any dimension.

Affiliated with

Also associated with

No associations

Rating

Relative Density of the Random r-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association (Technical Report) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Relative Density of the Random r-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association (Technical Report), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Relative Density of the Random r-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association (Technical Report) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-440396