Author:
Diananda P. H.,Bartlett M. S.
Abstract
In fundamental papers Bernstein (3) and Loève(8) have proved central limit theorems for wide classes of dependent variables. Their theorems are stated in terms of conditional distributions. In the case of dn-dependent variables (see § 3) they assume the existence, as the ‘conditioning’ variates vary, of finite upper bounds for certain conditional absolute moments higher than the second. More recently, Hoeffding and Robbins (7) have proved central limit theorems for m-dependent variables with finite third absolute moments, and Moran(10) has given a direct generalization of the Lindeberg-Lévy theorem for stationary discrete linear scalar processes.
Publisher
Cambridge University Press (CUP)
Reference12 articles.
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3. Étude asymptotique des sommes de variables aléatoires liées;Loève;J. Math. pures appl,1945
4. The central limit theorem for dependent random variables
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