Exact bounds on the truncated-tilted mean, with applications
Document Type
Article
Publication Date
1-1-2019
Abstract
© 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.
Publication Title
Theory of Probability and its Applications
Recommended Citation
Pinelis, I.
(2019).
Exact bounds on the truncated-tilted mean, with applications.
Theory of Probability and its Applications,
63(3), 447-463.
http://doi.org/10.1137/S0040585X97T989167
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/12343