A set-indexed process in a two-region image

Hans-Georg Müller and Kai-Sheng Song

Stochastic Processes and their Applications, 1996, vol. 62, issue 1, 87-101

Abstract: We investigate the problem of edge estimation in a two-region image in the setting of a fixed design regression model. The edge estimation problem is equivalent to estimating one of the plateau sets where the regression function is constant, and we define a global set-valued estimator by finding the partition which maximizes a weighted distance measure. An investigation of the weak convergence of the random sets generated by this estimator shows that a properly scaled stochastic process in symmetric differences between estimated and true partitions converges in the limit to a set-indexed Brownian motion with drift in d.

Keywords: Boundary; estimation; Brownian; motion; on; d; Change-point; Discontinuity; Edge; estimation; Gaussian; process; Pixel; Random; set; Weak; convergence (search for similar items in EconPapers)
Date: 1996
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(95)00094-1
Full text for ScienceDirect subscribers only

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:eee:spapps:v:62:y:1996:i:1:p:87-101

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().