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The central limit theorem for m-dependent variables asymptotically stationary to second order

Published online by Cambridge University Press:  24 October 2008

P. H. Diananda
P. H. Diananda
Affiliation:
Department of MathematicsUniversity of Malaya
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Extract

In a recent paper (3) the Lindeberg-Lévy theorem (2) was extended for certain types of stationary dependent variables. In the present paper mainly the same basic ideas as were used in (3) are employed to give central limit theorems for m-dependent scalar variables (a) stationary to second order and (b) asymptotically stationary to second order, the sufficient condition in each case being akin to the Linde-berg condition ((1), p. 57) for independent variables. The analogue of the main theorem for vector variables is given. An extension of the Lindeberg-Lévy theorem is derived.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 2 , April 1954 , pp. 287 - 292
Copyright
Copyright © Cambridge Philosophical Society 1954

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References

REFERENCES

(1)Cramér, H.Random variables and probability distributions (Cambridge, 1937).Google Scholar
(2)Cramér, H.Mathematical methods of statistics (Princeton, 1946), p. 215.Google Scholar
(3)Diananda, P. H.Some probability limit theorems with statistical applications. Proc. Camb. phil. Soc. 49 (1953), 239–46.CrossRefGoogle Scholar