Law of the iterated logarithm for self-normalized sums and their increments
2006 ◽
Vol 43
(1)
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pp. 79-114
Keyword(s):
Let X1, X2,… be independent, but not necessarily identically distributed random variables in the domain of attraction of a stable law with index 0<a<2. This paper uses Mn=max 1?i?n|Xi| to establish a self-normalized law of the iterated logarithm (LIL) for partial sums. Similarly self-normalized increments of partial sums are studied as well. In particular, the results of self-normalized sums of Horváth and Shao[9]under independent and identically distributed random variables are extended and complemented. As applications, some corresponding results for self-normalized weighted sums of iid random variables are also concluded.
1974 ◽
Vol 2
(6)
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pp. 1108-1138
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Keyword(s):
Keyword(s):
1990 ◽
Vol 3
(2)
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pp. 135-140
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2006 ◽
Vol 2006
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pp. 1-7
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Keyword(s):
2016 ◽
Vol 48
(3)
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pp. 672-690
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2012 ◽
Vol 12
(01)
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pp. 1150002
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1980 ◽
Vol 21
(3)
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pp. 373-391
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1987 ◽
Vol 101
(2)
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pp. 301-312
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1980 ◽
Vol 30
(1)
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pp. 5-14
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