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Laws of Large Numbers for Exchangeable Random Sets in Kuratowski-Mosco Sense

2006; Taylor & Francis; Volume: 24; Issue: 2 Linguagem: Inglês

10.1080/07362990500522114

1532-9356

Hiroshi Inoué, Robert L. Taylor,

Multi-Criteria Decision Making

Abstract Most of the results for laws of large numbers based on Banach space valued random sets assume that the sets are independent and identically distributed (IID) and compact, in which Rådström embedding or the refined method for collection of compact and convex subsets of a Banach space plays an important role. In this paper, exchangeability among random sets as a dependency, instead of IID, is assumed in obtaining strong laws of large numbers, since some kind of dependency of random variables may be often required for many statistical analyses. Also, the Hausdorff convergence usually used is replaced by another topology, Kuratowski-Mosco convergence. Thus, we prove strong laws of large numbers for exchangeable random sets in Kuratowski-Mosco convergence, without assuming the sets are compact, which is weaker than Hausdorff sense.