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Exact bounds on the truncated-tilted mean, with applications

Published 18 Mar 2011 in math.PR, math.ST, and stat.TH | (1103.3683v2)

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.

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