The distribution of the relative arc density of a family of interval catch digraph based on uniform data
We study a family of interval catch digraph called proportional-edge proximity catch digraph (PCD) which is also a special type of intersection digraphs parameterized with an expansion and a centrality parameter. PCDs are random catch digraphs that have been developed recently and have applications in classification and spatial pattern analysis. We investigate a graph invariant of the PCDs called relative arc density. We demonstrate that relative arc density of PCDs is a U-statistic and using the central limit theory of U-statistics, we derive the (asymptotic) distribution of the relative arc density of proportional-edge PCD for uniform data in one dimension. We also determine the parameters for which the rate of convergence to asymptotic normality is fastest. Copyright Springer-Verlag 2012
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 75 (2012)
Issue (Month): 6 (August)
|Contact details of provider:|| Web page: http://www.springerlink.com/link.asp?id=102509 |
|Order Information:||Web: http://link.springer.de/orders.htm|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ceyhan, Elvan & Priebe, Carey E., 2005. "The use of domination number of a random proximity catch digraph for testing spatial patterns of segregation and association," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 37-50, June.
- Priebe, Carey E. & DeVinney, Jason G. & Marchette, David J., 2001. "On the distribution of the domination number for random class cover catch digraphs," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 239-246, December.
- Priebe, Carey E. & Solka, Jeffrey L. & Marchette, David J. & Clark, B. Ted, 2003. "Class cover catch digraphs for latent class discovery in gene expression monitoring by DNA microarrays," Computational Statistics & Data Analysis, Elsevier, vol. 43(4), pages 621-632, August.
When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:75:y:2012:i:6:p:761-793. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn)or (Christopher F Baum)
If references are entirely missing, you can add them using this form.