Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables

被引：0
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作者：
Tapas K. Chandra
Deli Li
Andrew Rosalsky
机构：
[1] Indian Statistical Institute,Applied Statistics Division
[2] Lakehead University,Department of Mathematical Sciences
[3] University of Florida,Department of Statistics
来源：
Journal of Inequalities and Applications | / 2018卷
关键词：
Array of rowwise pairwise negative quadrant dependent random variables; Pairwise independent random variables; Weighted averages; Degenerate mean convergence; Stochastic domination; Almost sure convergence; 60F25; 60F99; 60F05;
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摘要：
For arrays of rowwise pairwise negative quadrant dependent random variables, conditions are provided under which weighted averages converge in mean to 0 thereby extending a result of Chandra, and conditions are also provided under which normed and centered row sums converge in mean to 0. These results are new even if the random variables in each row of the array are independent. Examples are provided showing (i) that the results can fail if the rowwise pairwise negative quadrant dependent hypotheses are dispensed with, and (ii) that almost sure convergence does not necessarily hold.
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