EconPapers    
Economics at your fingertips  
 

Self-crossing Points of a Line Segment Process

Zbyněk Pawlas ()
Additional contact information
Zbyněk Pawlas: Charles University in Prague

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 2, 295-309

Abstract: Abstract This paper is devoted to planar stationary line segment processes. The segments are assumed to be independent, identically distributed, and independent of the locations (reference points). We consider a point process formed by self-crossing points between the line segments. Its asymptotic variance is explicitly expressed for Poisson segment processes. The main result of the paper is the central limit theorem for the number of intersection points in expanding rectangular sampling window. It holds not only for Poisson processes of reference points but also for stationary point processes satisfying certain conditions on absolute regularity (β-mixing) coefficients. The proof is based on the central limit theorem for β-mixing random fields. Approximate confidence intervals for the intensity of intersections can be constructed.

Keywords: Absolute regularity coefficient; Asymptotic variance; Central limit theorem; Independent marking; Intensity of intersections; Poisson process; Segment process; 60D05; 60F05; 60G55; 62G20 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2) Track citations by RSS feed

Downloads: (external link)
http://link.springer.com/10.1007/s11009-012-9315-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-012-9315-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-012-9315-6

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2022-05-12
Handle: RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-012-9315-6