Remarks on uniform convergence of random variables and statistics

Convergence in distribution, convergece in probability, and convergence almost surely, , 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...

Full description

Saved in:
Bibliographic Details
Published inDemonstratio mathematica Vol. 45; no. 2; pp. 265 - 274
Main Authors Niemiro, Wojciech, Zieliński, Ryszard
Format Journal Article
LanguageEnglish
Published De Gruyter Open 01.06.2012
Subjects
60F05
62B99
62E20
Online AccessGet full text

Cover

More Information
Summary:Convergence in distribution, convergece in probability, and convergence almost surely, , 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.
ISSN:2391-4661
2391-4661
DOI:10.1515/dema-2013-0381