Exact bounds on the truncated-tilted mean, with applications

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© 2019 Society for Industrial and Applied Mathematics. Exact upper bounds for EXe h(X∧w) /Ee h(X∧w) , which is the expectation of the Cramér transform of the so-called Winsorized-tilted mean of a random variable, are given in terms of its first two moments. Such results are needed in work with 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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Theory of Probability and its Applications