Moment equalities for sums of random variables via integer partitions and Faà di Bruno's formula

Research output: Contribution to journalResearch articleContributedpeer-review



We give moment equalities for sums of independent and identically distributed random variables including, in particular, centered and specifically symmetric summands. Two different types of proofs, combinatorial and analytical, lead to 2 different types of formulas. Furthermore, the combinatorial method allows us to find the optimal lower and upper constants in the Marcinkiewicz-Zygmund inequalities in the case of even moment-orders. Our results are applied to give elementary proofs of the classical central limit theorem (CLT) and of the CLT for the empirical bootstrap. Moreover, we derive moment and exponential inequalities for self-normalized sums.


Original languageEnglish
Pages (from-to)558-575
Number of pages18
JournalTurkish journal of mathematics
Issue number3
Publication statusPublished - 2014


ASJC Scopus subject areas


  • Bootstrap, Faà di bruno's chain rule, Integer partitions, Marcinkiewicz-Zygmund inequalities, Moments, Self-normalized sums

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