Some limit theorems for m -pairwise negative quadrant dependent random variables

Yongfeng Wu; Jiangyan Peng

Kybernetika (2018)

  • Volume: 54, Issue: 4, page 815-828
  • ISSN: 0023-5954

Abstract

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The authors first establish the Marcinkiewicz-Zygmund inequalities with exponent p ( 1 ≤ p ≤ 2 ) 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.

How to cite

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Wu, Yongfeng, and Peng, Jiangyan. "Some limit theorems for $m$-pairwise negative quadrant dependent random variables." Kybernetika 54.4 (2018): 815-828. <http://eudml.org/doc/294740>.

@article{Wu2018,
abstract = {The authors first establish the Marcinkiewicz-Zygmund inequalities with exponent $p$ ($1\le p\le 2$) 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.},
author = {Wu, Yongfeng, Peng, Jiangyan},
journal = {Kybernetika},
keywords = {$m$-pairwise negative quadrant dependent; Marcinkiewicz–Zygmund inequality; $L^r$ convergence; complete convergence},
language = {eng},
number = {4},
pages = {815-828},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Some limit theorems for $m$-pairwise negative quadrant dependent random variables},
url = {http://eudml.org/doc/294740},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Wu, Yongfeng
AU - Peng, Jiangyan
TI - Some limit theorems for $m$-pairwise negative quadrant dependent random variables
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 4
SP - 815
EP - 828
AB - The authors first establish the Marcinkiewicz-Zygmund inequalities with exponent $p$ ($1\le p\le 2$) 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.
LA - eng
KW - $m$-pairwise negative quadrant dependent; Marcinkiewicz–Zygmund inequality; $L^r$ convergence; complete convergence
UR - http://eudml.org/doc/294740
ER -

References

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