Exact Rosenthal-type inequalities for p=3, and related results
Iosif Pinelis
TL;DR
This paper derives an exact Rosenthal-type inequality for third absolute moments and explores related results, which are useful for improving Berry--Esseen bounds in probability theory.
Contribution
It provides a precise inequality for third moments and related results, advancing the understanding of moment inequalities in probability.
Findings
Exact Rosenthal-type inequality for p=3 established
Related inequalities and bounds derived
Applications to Berry--Esseen bounds demonstrated
Abstract
An exact Rosenthal-type inequality for the third absolute moments is given, as well as a number of related results. Such results are useful in applications to Berry--Esseen bounds.
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Taxonomy
TopicsMathematical Inequalities and Applications · Random Matrices and Applications · Point processes and geometric inequalities