The central limit theorem for m-dependent variables
1955 ◽
Vol 51
(1)
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pp. 92-95
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Keyword(s):
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.
1954 ◽
Vol 50
(2)
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pp. 287-292
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2011 ◽
Vol 11
(01)
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pp. 71-80
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2006 ◽
Vol 15
(1)
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pp. 143-158
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Keyword(s):
2005 ◽
Vol 42
(2)
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pp. 173-194
1954 ◽
Vol 5
(6)
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pp. 987-987
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Keyword(s):