Weakly approaching sequences of random distributions
2000 (English)Report (Refereed)
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.
Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2000. Vol. 37, no 3, 17 p.807-822 p.
, Research report / Department of mathematical statistics, ISSN 1401-730X ; 8
Weak convergence, weakly approaching sequences, resampling, bootstrap, continuity theorem, Lévy metric, uniform metric
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:umu:diva-87444DOI: 10.1239/jap/1014842838ISI: 000165452900017OAI: oai:DiVA.org:umu-87444DiVA: diva2:709344