Modified Bernstein's inequality for sums of independent random variables
M.R.Formica, E.Ostrovsky, L.Sirota
TL;DR
This paper presents a modified version of Bernstein's inequality tailored for sums of independent centered random variables, utilizing relative tails or moments, and demonstrates the exactness of these new bounds through examples.
Contribution
The paper introduces a novel modification of Bernstein's inequality based on relative tails or moments, with proofs of exactness via illustrative examples.
Findings
New Bernstein's inequality version for tail/moment conditions
Examples confirming the bounds are tight and exact
Enhanced understanding of sum behavior of independent variables
Abstract
We modify the classical Bernstein's inequality for the sums of independent centered random variables (r.v.) in the terms of relative tails or moments. We built also some examples in order to show the exactness of offered results.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Bayesian Methods and Mixture Models · Random Matrices and Applications