On Hoeffding’s Inequalities1 by Vidmantas Bentkus

@inproceedings{Bentkus2004OnHI,
  title={On Hoeffding’s Inequalities1 by Vidmantas Bentkus},
  author={Vidmantas Bentkus},
  year={2004}
}
  • Vidmantas Bentkus
  • Published 2004
In a celebrated work by Hoeffding [J. Amer. Statist. Assoc. 58 (1963) 13–30], several inequalities for tail probabilities of sums Mn = X1 + · · · + Xn of bounded independent random variables Xj were proved. These inequalities had a considerable impact on the development of probability and statistics, and remained unimproved until 1995 when Talagrand [Inst. Hautes Études Sci. Publ. Math. 81 (1995a) 73–205] inserted certain missing factors in the bounds of two theorems. By similar factors, a… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 17 references

Fractional sums and integrals of r-concave tails and applications to comparison probability inequalities

  • I. PINELIS
  • In Advances in Stochastic Inequalities…
  • 1999
Highly Influential
4 Excerpts

Über eine Klasse von Mittelbildungen mit Anwendungen auf die Determinantentheorie

  • I. SCHUR
  • Sitzungsber. Berlin Math. Ges
  • 1923
Highly Influential
8 Excerpts

Optimal tail comparison based on comparison of moments

  • I. PINELIS
  • In High Dimensional Probability. Progress in…
  • 1998
Highly Influential
2 Excerpts

The missing factor in Hoeffding’s inequalities

  • M. TALAGRAND
  • Ann. Inst. H. Poincaré Probab. Statist
  • 1995
Highly Influential
3 Excerpts

Extremal probabilistic problems and Hotelling’s T 2 test under a symmetry assumption

  • I. PINELIS
  • Ann. Statist
  • 1994
Highly Influential
2 Excerpts

A probability inequality for linear combinations of bounded random variables

  • M. L. 1223–1226. EATON
  • 1974
Highly Influential
2 Excerpts

Sur quelques applications des fonctions convexes et concave au sens de I

  • A. OSTROWSKI
  • Schur. J. Math. Pures Appl
  • 1952
Highly Influential
1 Excerpt

Some comments on deviation probabilities for infinitely divisible random vectors

  • V. PAULAUSKAS
  • Lithuanian Math. J
  • 2002
1 Excerpt

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