Limiting behavior for arrays of row-wise upper extended negatively dependent random variables

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Abstract

Our aim is to obtain deterministic bounds for the row sum elements of a random triangular array introducing, thereunto, a dependence structure for triangular arrays of random variables which extend the concepts of upper and lower extended negatively dependence already known for random variables. Concretely, for triangular arrays { Xn, k, 1 ≦ k≦ n, n≧ 1 } of row-wise upper extended negatively dependent random variables with dominating sequence { Mn, n≧ 1 } weakly mean dominated by a random variable X and sequences { bn} of positive constants, conditions are stated to ensure the deterministic boundedness of Σ k= 1 n(Xn, k- EXn, k) / bnLog n, where Log n: = log max { n, e}. In particular, a sufficient moment condition is given permitting us to achieve our goal under the rate of the so called “Law of the Logarithm”.

Original languageEnglish
Pages (from-to)481-492
Number of pages12
JournalActa Mathematica Hungarica
Volume148
Issue number2
DOIs
Publication statusPublished - 1 Apr 2016

Keywords

  • triangular array
  • upper extended negatively dependent random variable
  • law of the logarithm

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