On Laws of Large Numbers for Exchangeable Random Sets

摘要

Exchangeability as an alternative to the random sample being independent, identically distributed random variables gives the study of asymptotic properties of random variables, since some kind of dependency of random variables may be often required for many statistical analyses. Most of the results for Laws of Large Numbers based on Banach space valued random sets assume that the sets are compact, in which Radstroem embedding or the refined method for collection of compact and convex subsets of a Banach space plays an important role. This paper attempts to 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.