Geodesic
A moment inequality with application to convergence rate estimates in the global CLT for Poisson-binomial random sums
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 345-364

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A moment inequality between the central and noncentral third-order absolute moments is proved, which is optimal for every value of the recentering parameter. By use of this inequality there are constructed convergence rate estimates in the central limit theorem for Poisson-binomial random sums in the uniform and mean metrics.
Mots-clés : compound Poisson-binomial distribution
Keywords: central limit theorem (CLT), convergence rate estimate, normal approximation, Berry– Esséen inequality, moment inequality. 
@article{TVP_2017_62_2_a5,
     author = {I. G. Shevtsova},
     title = {A moment inequality with application to convergence rate estimates in the global {CLT} for {Poisson-binomial} random sums},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {345--364},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a5/}
}
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I. G. Shevtsova. A moment inequality with application to convergence rate estimates in the global CLT for Poisson-binomial random sums. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 2, pp. 345-364. http://geodesic.mathdoc.fr/item/TVP_2017_62_2_a5/