Abstract
Exact upper bounds on the Winsorised-tilted mean, E Xe h(X^ w) E eh(X^ w) , of a random variable X 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. AMS 2000 subject classifications: Primary 60E15; secondary 60E10, 60F10, 60F05. Keywords and phrases: exact upper bounds, Winsorization, truncation, large deviations, nonuniform Berry-Esseen bounds, Cramer tilt transform, monotonicity, Bayes posterior mean.
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