Exact bounds on the truncated-tilted mean, with applications
arXiv:1103.3683
Abstract
Exact upper bounds on the Winsorised-tilted mean of a random variable in terms of its first two moments are given. Such results are needed in work on nonuniform Berry--Esseen-type bounds for general nonlinear statistics. As another application, optimal upper bounds on the Bayes posterior mean are provided. Certain monotonicity properties of the tilted mean are also presented.
Proposition 2.6(II) is slightly generalized