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- Title
ON THE CENTRAL LIMIT PROBLEM FOR PARTIALLY EXCHANGEABLE RANDOM VARIABLES WITH VALUES IN A HILBERT SPACE.
- Authors
Regazzini, E.; Sazonov, V.V
- Abstract
This paper deals with a central limit problem for columnwise exchangeable arrays of a Hilbert space valued random variables satisfying the condition of conditional uniform asymptotic negligibility. It is proved that rowwise sums may converge in distribution only to an exchangeable sequence of random variables whose distribution is a mixture of in nitely divisible distributions. Conditions for convergence to a speci c distribution and, in particular, to a mixture of Gaussian distributions, are also given.
- Subjects
HILBERT space; GAUSSIAN distribution; RANDOM variables; ASYMPTOTIC expansions
- Publication
Theory of Probability & Its Applications, 1998, Vol 42, Issue 4, p656
- ISSN
0040-585X
- Publication type
Article
- DOI
10.1137/S0040585X97976520