Abstract
For triangular arrays {Xn,k : 1 ≤ k ≤ n, n ≥ 1} of upper extended negatively dependent random variables weakly mean dominated by a random variable X and sequences {bn} of positive constants, conditions are given to guarantee an almost sure finite upper bound to ∑k=1n(Xn,k - EXn,k)/√bn Log n, where Log n := max{1, log n}, thus getting control over the limiting rate in terms of the prescribed sequence {bn} and permitting us to weaken or strengthen the assumptions on the random variables.
Original language | English |
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Pages (from-to) | 159-167 |
Number of pages | 9 |
Journal | Bulletin Of The Australian Mathematical Society |
Volume | 92 |
Issue number | 1 |
DOIs | |
Publication status | Published - 6 Jul 2015 |
Keywords
- Bernstein inequality
- law of the logarithm
- upper extended negatively dependent arrays