The central limit theorem for m-dependent variables
- 1 January 1955
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 51 (1) , 92-95
- https://doi.org/10.1017/s0305004100029959
Abstract
In a previous paper (4) central limit theorems were obtained for sequences of m-dependent random variables (r.v.'s) asymptotically stationary to second order, the sufficient conditions being akin to the Lindeberg condition (3). In this paper similar theorems are obtained for sequences of m-dependent r.v.'s with bounded variances and with the property that for large n, where s′n is the standard deviation of the nth partial sum of the sequence. The same basic ideas as in (4) are used, but the proofs have been simplified. The results of this paper are examined in relation to earlier ones of Hoeffding and Robbins(5) and of the author (4). The cases of identically distributed r.v.'s and of vector r.v.'s are mentioned.Keywords
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- Some probability limit theorems with statistical applicationsMathematical Proceedings of the Cambridge Philosophical Society, 1953
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