Abstract
Many years ago Hoeffding (1956, Theorem 3) proved the following result: if X1,…, Xn are independent Bernoulli random variables and if
is (strictly) concave, then
where on the right-hand side it is assumed that ℙ(Xi=1)=pi while on the left-hand side \(P({X_i} = 1) = \bar p = (1/n)\sum\nolimits_{i = 1}^n {{p_i}}\) for all i = 1,…, n.
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© 1984 Springer Science+Business Media New York
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Berg, C., Christensen, J.P.R., Ressel, P. (1984). Hoeffding’s Inequality and Multivariate Majorization. In: Harmonic Analysis on Semigroups. Graduate Texts in Mathematics, vol 100. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1128-0_7
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DOI: https://doi.org/10.1007/978-1-4612-1128-0_7
Publisher Name: Springer, New York, NY
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