Exact bounds on the truncated-tilted mean, with applications
Probability
2012-05-24 v2 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1103.3683,
title = {Exact bounds on the truncated-tilted mean, with applications},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:1103.3683},
year = {2012}
}
Comments
Proposition 2.6(II) is slightly generalized