关于行向两两负象限相依随机变量阵列的一些均值收敛定理。
Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables.
作者信息
Chandra Tapas K, Li Deli, Rosalsky Andrew
机构信息
1Applied Statistics Division, Indian Statistical Institute, Kolkata, India.
2Department of Mathematical Sciences, Lakehead University, Thunder Bay, Canada.
出版信息
J Inequal Appl. 2018;2018(1):221. doi: 10.1186/s13660-018-1811-y. Epub 2018 Aug 23.
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.
对于逐行成对负象限相依随机变量的阵列，给出了加权平均值依均值收敛到0的条件，从而推广了钱德拉的一个结果，还给出了标准化且中心化的行和依均值收敛到0的条件。即使阵列每行中的随机变量是独立的，这些结果也是新的。给出的例子表明：（i）如果摒弃逐行成对负象限相依假设，结果可能不成立；（ii）几乎必然收敛不一定成立。
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