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Records in subsets of a random field
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2013 (English)In: Statistics and Probability Letters, ISSN 0167-7152, E-ISSN 1879-2103, Vol. 83, no 3, 689-699 p.Article in journal (Refereed) Published
Abstract [en]

Consider an i.i.d.random field {Xk:k∈Z+d}, together with a sequence of unboundedly increasing nested sets Sj={n-ary union}k=1jHk,j≥1, where the sets H j are disjoint. The canonical example consists of the hyperbolas Hj={k∈Z+d:{pipe}k{pipe}=j}. We are interested in the number of "hyperbolas" H j that contain at least one record, and, furthermore, the number of records on the "next hyperbola", that is, the number of observations on H j that exceed max { Xk : k ∈ S j -1 } Various limit theorems under mild conditions on the size of the sets H j are presented.

Place, publisher, year, edition, pages
2013. Vol. 83, no 3, 689-699 p.
Keyword [en]
Central limit theorem, I.i.d.random variables, Law of large numbers, Random field, Records
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:uu:diva-191976DOI: 10.1016/j.spl.2012.11.015ISI: 000316505200003OAI: oai:DiVA.org:uu-191976DiVA: diva2:600729
Available from: 2013-01-25 Created: 2013-01-15 Last updated: 2017-12-06Bibliographically approved

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Gut, Allan

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