The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Bentkus, V. A remark on the inequalities of Bernstein, Prokhorov, Bennett, Hoeffding, and Talagrand. (Russian) Liet. Mat. Rink. 42 (2002), no. 3, 332--342; translation in Lithuanian Math. J. 42 (2002), no. 3, 262--269 MR1947624
  • Bentkus, Vidmantas. On Hoeffding's inequalities. Ann. Probab. 32 (2004), no. 2, 1650--1673. MR2060313
  • Bentkus, Vidmantas. On measure concentration for separately Lipschitz functions in product spaces. Israel J. Math. 158 (2007), 1--17. MR2342455
  • 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
  • Gilardoni, Gustavo L. An improvement on Vajda's inequality. In and out of equilibrium. 2, 299--304, Progr. Probab., 60, Birkhäuser, Basel, 2008. MR2477387
  • Hoeffding, Wassily. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 1963 13--30. MR0144363
  • Kearns, M. J. and Saul, L. K. Large deviation methods for approximate probabilistic inference. In UAI, 1998.
  • Krafft, O. A note on exponential bounds for binomial probabilities. Annals of the Institute of Statistical Mathematics 21, (1969), 219-220. Zbl 0176.49106
  • McDiarmid, Colin. On the method of bounded differences. Surveys in combinatorics, 1989 (Norwich, 1989), 148--188, London Math. Soc. Lecture Note Ser., 141, Cambridge Univ. Press, Cambridge, 1989. MR1036755
  • McDiarmid, Colin. Concentration. Probabilistic methods for algorithmic discrete mathematics, 195--248, Algorithms Combin., 16, Springer, Berlin, 1998. MR1678578
  • Owhadi, H., Sullivan, T. J., McKerns, M., Ortiz, M. and Scovel, C. Optimal Uncertainty Quantification. arXiv: 1009.0679v3. Math. PR. 2012.
  • Pinelis, Iosif. On normal domination of (super)martingales. Electron. J. Probab. 11 (2006), no. 39, 1049--1070. MR2268536
  • Pinelis, Iosif. Binomial upper bounds on generalized moments and tail probabilities of (super)martingales with differences bounded from above. High dimensional probability, 33--52, IMS Lecture Notes Monogr. Ser., 51, Inst. Math. Statist., Beachwood, OH, 2006. MR2387759
  • Sion, Maurice. On general minimax theorems. Pacific J. Math. 8 1958 171--176. MR0097026
  • Topsøe, Flemming. Bounds for entropy and divergence for distributions over a two-element set. JIPAM. J. Inequal. Pure Appl. Math. 2 (2001), no. 2, Article 25, 13 pp. (electronic). MR1873865
  • Vajda, Igor. Note on discrimination information and variation. IEEE Trans. Information Theory IT-16 1970 771--773. MR0275575

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