Geodesic
Exact bounds on the truncated-tilted mean, with applications
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 545-564 Cet article a éte moissonné depuis la source Math-Net.Ru

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Exact upper bounds for ${\mathbf{E} Xe^{h(X\wedge w)}}/{\mathbf{E} e^{h(X\wedge w)}}$, 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.
Keywords: exact bound, Winsorization, truncation, large deviation, nonuniform Berry–Esseen-type bounds, monotonicity, Bayes posterior mean.
Mots-clés : Cramér transform 
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I. Pinelis. Exact bounds on the truncated-tilted mean, with applications. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 545-564. http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a7/

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