Relative Density of the Random $r$-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association

Details Relative Density of the Random $r$-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association Relative Density of the Random $r$-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association

2008-02-05

arxiv.org/abs/0802.0622v1

Computational Statistics & Data Analysis (2006), 50(8):1925-1964

Statistics

Methodology

29 pages, 21 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 efficacies, and selection of the proximity map parameter to optimize efficiency. Furthermore 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 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, 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 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-45832