Extensions of the Hoeffding-Azuma inequalities

Emmanuel Rio (University of Versailles)

Abstract


In this paper we give extensions of the Hoeffding-Azuma inequalities for weighted sums of uniformly bounded martingale differences.


Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 1-6

Publication Date: July 6, 2013

DOI: 10.1214/ECP.v18-2690

References

  • Antonov, S. N. Probability inequalities for a series of independent random variables. (Russian) Teor. Veroyatnost. i Primenen. 24 (1979), no. 3, 632-636. MR0541380
  • Azuma, Kazuoki. Weighted sums of certain dependent random variables. Tôhoku Math. J. (2) 19 1967 357-367. MR0221571
  • Bentkus, Vidmantas. On Hoeffding's inequalities. Ann. Probab. 32 (2004), no. 2, 1650-1673. MR2060313
  • Devroye, Luc; Lugosi, Gábor. Combinatorial methods in density estimation. Springer Series in Statistics. Springer-Verlag, New York, 2001. xii+208 pp. ISBN: 0-387-95117-2 MR1843146
  • Hoeffding, Wassily. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 1963 13-30. MR0144363
  • Krafft, O. A note on exponential bounds for binomial probabilities. Annals of the Institute of Statistical Mathematics 21, (1969), 219-220. Zbl 0176-49106.
  • Rio, E. On McDiarmid's concentration inequality. Electron. Commun. Probab. 18, (2013), no. 44, 1-11.
  • Whittle, P. Refinements of Kolmogorov's inequality. Teor. Verojatnost. i Primenen. 14 1969 315-317. MR0246353
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.