Some probability limit theorems with statistical applications
1953 ◽
Vol 49
(2)
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pp. 239-246
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Keyword(s):
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.
1987 ◽
Vol 76
(1)
◽
pp. 1-13
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2002 ◽
Vol 38
(3)
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pp. 341-384
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Keyword(s):
1983 ◽
Vol 63
(4)
◽
pp. 555-555
◽
1981 ◽
Vol 57
(4)
◽
pp. 509-534
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Keyword(s):
Keyword(s):
2015 ◽
Vol 125
(2)
◽
pp. 428-457
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