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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 3, Pages 587–609
DOI: https://doi.org/10.4213/tvp5123 (Mi tvp5123) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Moment inequalities for $m$-NOD random variables and their applications

X. Wanga, Sh. H. Hua, A. I. Volodinb

a School of Mathematical Sciences, Anhui University, China
b Department of Mathematics and Statistics, University of Regina, Regina, Canada
Full-text PDF (538 kB) Citations (10)
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DOI: https://doi.org/10.4213/tvp5123
Abstract: The concept of $m$-negatively orthant dependent ($m$-NOD) random variables is introduced, and the moment inequalities for $m$-NOD random variables, especially the Marcinkiewicz–Zygmund-type inequality and Rosenthal-type inequality, are established. As one application of the moment inequalities, we study the $L_r$ convergence and strong convergence for $m$-NOD random variables under some uniformly integrable conditions. On the other hand, the asymptotic approximation of inverse moments for nonnegative $m$-NOD random variables with finite first moments is established. The results obtained in the paper generalize or improve some known ones for independent sequences and some dependent sequences.
Keywords: $m$-negatively orthant dependent sequence, $L_r$-convergence, inverse moments, Marcinkiewicz–Zygmund-type inequalities, Rosenthal inequality.
Funding agency Grant number
National Natural Science Foundation of China 11671012
11501004
11501005
Natural Science Foundation of Anhui Province 1508085J06
Key Projects for Academic Talent of Anhui Province gxbjZD2016005
This work was supported by the National Natural Science Foundation of China (11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06), and the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005).
Received: 31.03.2015
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 3, Pages 471–490
DOI: https://doi.org/10.1137/S0040585X97T988745
Bibliographic databases:
Document Type: Article
Language: English
Citation: X. Wang, Sh. H. Hu, A. I. Volodin, “Moment inequalities for $m$-NOD random variables and their applications”, Teor. Veroyatnost. i Primenen., 62:3 (2017), 587–609; Theory Probab. Appl., 62:3 (2018), 471–490
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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