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
AN - SCOPUS:84958772713
VL - 148
SP - 481
EP - 492
JO - Acta Mathematica Hungarica
JF - Acta Mathematica Hungarica
SN - 0236-5294
IS - 2
ER -