Sharp Rosenthal-type inequalities for mixtures and log-concave variables

Abstract

We obtain Rosenthal-type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremisers in log-concave settings when the moments of summands are individually constrained.

15 pages. Final version (referee comments incorporated). To appear in Bull. Lond. Math. Soc

References in corpus (2)

• Gaussian mixtures: entropy and geometric inequalities
• Exact inequalities for sums of asymmetric random variables, with applications