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Some probability limit theorems with statistical applications

Published online by Cambridge University Press:  24 October 2008

P. H. Diananda  and
M. S. Bartlett
P. H. Diananda
Affiliation:
Department of MathematicsUniversity of Malaya
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Extract

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.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 2 , April 1953 , pp. 239 - 246
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

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