Second-Order Properties for Planar Mondrian Tessellations

Carina Betken (), Tom Kaufmann (), Kathrin Meier () and Christoph Thäle ()
Additional contact information
Carina Betken: Ruhr University Bochum
Tom Kaufmann: Ruhr University Bochum
Kathrin Meier: Ruhr University Bochum
Christoph Thäle: Ruhr University Bochum

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 2, 1-28

Abstract: Abstract In this paper planar STIT tessellations with weighted axis-parallel cutting directions are considered. They are known also as weighted planar Mondrian tessellations in the machine learning literature, where they are used in random forest learning and kernel methods. Various second-order properties of such random tessellations are derived, in particular, explicit formulas are obtained for suitably adapted versions of the pair- and cross-correlation functions of the length measure on the edge skeleton and the vertex point process. Also, explicit formulas and the asymptotic behaviour of variances are discussed in detail.

Keywords: Cross-correlation function; Mondrian tessellation; Pair-correlation function; STIT tessellation; Stochastic geometry; Variance asymptotic; 60D05 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-023-10017-2 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:25:y:2023:i:2:d:10.1007_s11009-023-10017-2

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

DOI: 10.1007/s11009-023-10017-2

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 ().