Complete convergence for weighted sums of arrays of random elements
1983 ◽
Vol 6
(1)
◽
pp. 69-79
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Keyword(s):
Let{Xnk:k,n=1,2,…}be an array of row-wise independent random elements in a separable Banach space. Let{ank:k,n=1,2,…}be an array of real numbers such that∑k=1∞|ank|≤1and∑n=1∞exp(−α/An)<∞for eachα ϵ R+whereAn=∑k=1∞ank2. The complete convergence of∑k=1∞ankXnkis obtained under varying moment and distribution conditions on the random elements. In particular, laws of large numbers follow for triangular arrays of random elements, and consistency of the kernel density estimates is obtained from these results.
1985 ◽
Vol 8
(1)
◽
pp. 135-144
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1987 ◽
Vol 10
(4)
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pp. 805-814
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1993 ◽
Vol 16
(3)
◽
pp. 587-591
◽
1993 ◽
Vol 6
(1)
◽
pp. 1-9
◽
2002 ◽
Vol 47
(3)
◽
pp. 533-547
◽
2003 ◽
Vol 47
(3)
◽
pp. 455-468
◽
2002 ◽
Vol 58
(2)
◽
pp. 185-194
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Keyword(s):
1979 ◽
Vol 2
(2)
◽
pp. 309-323
1994 ◽
Vol 17
(1)
◽
pp. 1-14
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Keyword(s):