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 language | English |
|---|---|
| Pages (from-to) | 481-492 |
| Number of pages | 12 |
| Journal | Acta Mathematica Hungarica |
| Volume | 148 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Apr 2016 |
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Keywords
- triangular array
- upper extended negatively dependent random variable
- law of the logarithm
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Limiting behavior for arrays of row-wise upper extended negatively dependent random variables. / Lita Da Silva, J.
In: Acta Mathematica Hungarica, Vol. 148, No. 2, 01.04.2016, p. 481-492.Research output: Contribution to journal › Article
TY - JOUR
T1 - Limiting behavior for arrays of row-wise upper extended negatively dependent random variables
AU - Lita Da Silva, J.
N1 - sem pdf conforme despacho.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - 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”.
AB - 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”.
KW - triangular array
KW - upper extended negatively dependent random variable
KW - law of the logarithm
UR - http://www.scopus.com/inward/record.url?scp=84958772713&partnerID=8YFLogxK
U2 - 10.1007/s10474-016-0585-2
DO - 10.1007/s10474-016-0585-2
M3 - Article
VL - 148
SP - 481
EP - 492
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
SN - 0236-5294
IS - 2
ER -