LIMITING BEHAVIOUR for ARRAYS of UPPER EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES

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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 languageEnglish
Pages (from-to)159-167
Number of pages9
JournalBulletin Of The Australian Mathematical Society
Volume92
Issue number1
DOIs
Publication statusPublished - 6 Jul 2015

Keywords

  • Bernstein inequality
  • law of the logarithm
  • upper extended negatively dependent arrays

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