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Weakly approaching sequences of random distributionsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2000 (English)Report (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Umeå: Umeå universitet , 2000. Vol. 37, no 3, 17 p.807-822 p.
##### Series

, Research report / Department of mathematical statistics, ISSN 1401-730X ; 8
##### Keyword [en]

Weak convergence, weakly approaching sequences, resampling, bootstrap, continuity theorem, Lévy metric, uniform metric
##### National Category

Probability Theory and Statistics
##### Identifiers

URN: urn:nbn:se:umu:diva-87444DOI: 10.1239/jap/1014842838ISI: 000165452900017OAI: oai:DiVA.org:umu-87444DiVA: diva2:709344
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Available from: 2014-04-01 Created: 2014-04-01 Last updated: 2014-10-21Bibliographically approved

We introduce the notion of *weakly approaching sequences of distributions*, which is a generalization of the well-known concept of weak convergence of distributions. The main difference is that the suggested notion does not demand the existence of a limit distribution. A similar definition for conditional (random) distributions is presented. Several properties of weakly approaching sequences are given. The tightness of some of them is essential. The Cramér-Lévy continuity theorem for weak convergence is generalized to weakly approaching sequences of (random) distributions. It has several applications in statistics and probability. A few examples of applications to resampling are given.

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