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Keywords:
$m$-pairwise negative quadrant dependent; Marcinkiewicz–Zygmund inequality; $L^r$ convergence; complete convergence
$m$-pairwise negative quadrant dependent; Marcinkiewicz–Zygmund inequality; $L^r$ convergence; complete convergence
Summary:
The authors first establish the Marcinkiewicz-Zygmund inequalities with exponent $p$ ($1\leq p\leq2$) for $m$-pairwise negatively quadrant dependent ($m$-PNQD) random variables. By means of the inequalities, the authors obtain some limit theorems for arrays of rowwise $m$-PNQD random variables, which extend and improve the corresponding results in [Y. Meng and Z. Lin (2009)] and [H. S. Sung (2013)]. It is worthy to point out that the open problem of [H. S. Sung, S. Lisawadi, and A. Volodin (2008)] can be solved easily by using the obtained inequality in this paper.
References:
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