Geodesic
Moment inequalities for $m$-NOD random variables and their applications
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 3, pp. 587-609

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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, Marcinkiewicz–Zygmund-type inequalities, Rosenthal inequality.
Mots-clés : $L_r$-convergence, inverse moments 
@article{TVP_2017_62_3_a7,
     author = {X. Wang and Sh. H. Hu and A. I. Volodin},
     title = {Moment inequalities for $m${-NOD} random variables and their applications},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {587--609},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_3_a7/}
}
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X. Wang; Sh. H. Hu; A. I. Volodin. Moment inequalities for $m$-NOD random variables and their applications. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 3, pp. 587-609. http://geodesic.mathdoc.fr/item/TVP_2017_62_3_a7/