An exact bound on the truncated-tilted mean for symmetric distributions

TL;DR

This paper establishes an exact upper bound on the Winsorised-tilted mean for symmetric distributions using their second moment, aiding in precise probabilistic bounds for nonlinear statistics.

Contribution

It provides a novel, exact bound on the truncated-tilted mean for symmetric distributions, enhancing the accuracy of probabilistic inequalities.

Findings

Derived an exact upper bound for symmetric distributions' Winsorised-tilted mean.

Applied the bound to improve nonuniform Berry--Esseen-type bounds.

Facilitated more precise analysis of nonlinear statistics.

Abstract

An exact upper bound on the Winsorised-tilted mean of a symmetric random variable in terms of its second moment is given. Such results are used in work on nonuniform Berry--Esseen-type bounds for general nonlinear statistics.