Exact bounds on the truncated-tilted mean, with applications

Understand

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.