Fold-up derivatives of set-valued functions and the change-set problem: A Survey

Estate Khmaladze () and Wolfgang Weil ()
Additional contact information
Estate Khmaladze: Victoria University of Wellington
Wolfgang Weil: Karlsruhe Institute of Technology

Annals of the Institute of Statistical Mathematics, 2018, vol. 70, issue 1, No 1, 38 pages

Abstract: Abstract We give a survey on fold-up derivatives, a notion which was introduced by Khmaladze (J Math Anal Appl 334:1055–1072, 2007) and extended by Khmaladze and Weil (J Math Anal Appl 413:291–310, 2014) to describe infinitesimal changes in a set-valued function. We summarize the geometric background and discuss in detail applications in statistics, in particular to the change-set problem of spatial statistics, and show how the notion of fold-up derivatives leads to the theory of testing statistical hypotheses about the change-set. We formulate Poisson limit theorems for the log-likelihood ratio in two versions of this problem and present also the route to a central limit theorem.

Keywords: Infinitesimal image analysis; Generalized functions; Fold-up derivatives; Local Steiner formula; Local point process; Set-valued mapping; Derivative set; Normal cylinder; Change-set problem (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10463-017-0628-7 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:aistmt:v:70:y:2018:i:1:d:10.1007_s10463-017-0628-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-017-0628-7

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().