Exact bounds on the truncated-tilted mean, with applications
Iosif Pinelis
TL;DR
This paper derives exact bounds on the Winsorised-tilted mean of a random variable using its first two moments, with applications in Berry--Esseen bounds and Bayesian posterior analysis.
Contribution
It provides the first precise upper bounds on the truncated-tilted mean based on moments, advancing nonuniform Berry--Esseen bounds and Bayesian inference methods.
Findings
Exact upper bounds on the Winsorised-tilted mean are established.
Monotonicity properties of the tilted mean are analyzed.
Applications include improved bounds in nonlinear statistics and Bayesian analysis.
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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Taxonomy
TopicsAdvanced Statistical Methods and Models · Mathematical Inequalities and Applications · Random Matrices and Applications