Remarks on uniform convergence of random variables and statistics
Abstract: Convergence in distribution, convergece in probability, and convergence almost surely, uniform with respect to a family of probability distributions, is considered. These concepts appeared to be appropriate tools for asymptotic theory of mathematical statistics and many partial results are scattered in the literature of the subject. The aim of this note is to present a unified review of the results in a general and abstract setup. We examine a few rather paradoxical examples which hopefully shed some light on the subtleties of the underlying definitions and the role of asymptotic approximations in statistics. A motivation for considering these problems is provided by their applications.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Remarks on uniform convergence of random variables and statistics ; volume:45 ; number:2 ; year:2012 ; pages:265-274 ; extent:10
Demonstratio mathematica ; 45, Heft 2 (2012), 265-274 (gesamt 10)
- Creator
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Niemiro, Wojciech
Zieliński, Ryszard
- DOI
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10.1515/dema-2013-0381
- URN
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urn:nbn:de:101:1-2411171657549.206856959342
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:27 AM CEST
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Associated
- Niemiro, Wojciech
- Zieliński, Ryszard
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