Article ID: | iaor20021369 |
Country: | United States |
Volume: | 17 |
Issue: | 2 |
Start Page Number: | 121 |
End Page Number: | 146 |
Publication Date: | Jan 2001 |
Journal: | Communications in Statistics - Stochastic Models |
Authors: | Rosenthal Jeffrey S., Roberts Gareth O. |
Keywords: | sets |
In this paper we examine the relationship between small sets and their generalisation, pseudo-small sets. We consider conditions which imply the equivalence of the two notions, and give examples where they are definitely different. We give further examples where sets are both pseudo-small and small, but the minorisation constants implied by the two notions are different. Applications of recent computable bounds results are given and extended. We also give a result linking the ideas of monotonicity and minorisation. Specifically we demonstrate that if a non-monotone chain satisfies a minorisation condition, and furthermore is stochastically dominated by a monotone chain which satisfies a Lyapunov drift condition, then a probability construction exists which incorporates both the bounding process and the minorisation condition.