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References

  • Bentkus, Vidmantas. On measure concentration for separately Lipschitz functions in product spaces. Israel J. Math. 158 (2007), 1--17. MR2342455
  • Bentkus, V. An inequality for tail probabilities of martingales with differences bounded from one side. J. Theoret. Probab. 16 (2003), no. 1, 161--173. MR1956826
  • Bentkus, Vidmantas. On Hoeffding's inequalities. Ann. Probab. 32 (2004), no. 2, 1650--1673. MR2060313
  • Bobkov, Sergey G.; Götze, Friedrich; Houdré, Christian. On Gaussian and Bernoulli covariance representations. Bernoulli 7 (2001), no. 3, 439--451. MR1836739
  • Dembo, Amir. Information inequalities and concentration of measure. Ann. Probab. 25 (1997), no. 2, 927--939. MR1434131
  • Eaton, Morris L. A note on symmetric Bernoulli random variables. Ann. Math. Statist. 41 1970 1223--1226. MR0268930
  • sc Eaton, M. L. (1974). A probability inequality for linear combinations of bounded random variables. Ann. Statist./~ 2, 609--614.
  • Edelman, David. An inequality of optimal order for the tail probabilities of the $t$-statistic under symmetry. J. Amer. Statist. Assoc. 85 (1990), no. 409, 120--122. MR1137357
  • Fuk, D. H. Certain probabilistic inequalities for martingales. (Russian) Sibirsk. Mat. Ž. 14 (1973), 185--193, 239. MR0326835
  • Fuk, D. H.; Nagaev, S. V. Probabilistic inequalities for sums of independent random variables. (Russian) Teor. Verojatnost. i Primenen. 16 (1971), 660--675. MR0293695
  • Graversen, S. E.; Peškir, G. Extremal problems in the maximal inequalities of Khintchine. Math. Proc. Cambridge Philos. Soc. 123 (1998), no. 1, 169--177. MR1474873
  • Haagerup, Uffe. The best constants in the Khintchine inequality. Studia Math. 70 (1981), no. 3, 231--283 (1982). MR0654838
  • Hoeffding, Wassily. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 1963 13--30. MR0144363
  • Karr, Alan F. Extreme points of certain sets of probability measures, with applications. Math. Oper. Res. 8 (1983), no. 1, 74--85. MR0703827
  • Khintchine, A. Über dyadische Brüche. (German) Math. Z. 18 (1923), no. 1, 109--116. MR1544623
  • Ledoux, Michel. Concentration of measure and logarithmic Sobolev inequalities. Séminaire de Probabilités, XXXIII, 120--216, Lecture Notes in Math., 1709, Springer, Berlin, 1999. MR1767995
  • 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
  • Nagaev, S. V. Large deviations of sums of independent random variables. Ann. Probab. 7 (1979), no. 5, 745--789. MR0542129
  • sc Pinelis, I. F. (1981). Limit theorems on large deviations for sums of independent random variables with Cramer's condition violated. (Russian) Deposited at VINITI (All-Russian Institute of Scientific and Technical Information for All-Union Institute of Scientific and Technical Information), No. 1674-81Dep., 94 pages.
  • Pinelis, I. F. Asymptotic equivalence of the probabilities of large deviations for sums and maximum of independent random variables. (Russian) Limit theorems of probability theory, 144--173, 176, Trudy Inst. Mat., 5, "Nauka'' Sibirsk. Otdel., Novosibirsk, 1985. MR0821760
  • Pinelis, Iosif. Extremal probabilistic problems and Hotelling's $T^ 2$ test under a symmetry condition. Ann. Statist. 22 (1994), no. 1, 357--368. MR1272088
  • Pinelis, Iosif. Optimum bounds for the distributions of martingales in Banach spaces. Ann. Probab. 22 (1994), no. 4, 1679--1706. MR1331198
  • Pinelis, Iosif. Optimal tail comparison based on comparison of moments. High dimensional probability (Oberwolfach, 1996), 297--314, Progr. Probab., 43, Birkhäuser, Basel, 1998. MR1652335
  • Pinelis, Iosif. Fractional sums and integrals of $r$-concave tails and applications to comparison probability inequalities. Advances in stochastic inequalities (Atlanta, GA, 1997), 149--168, Contemp. Math., 234, Amer. Math. Soc., Providence, RI, 1999. MR1694770
  • Pinelis, Iosif. On exact maximal Khinchine inequalities. High dimensional probability, II (Seattle, WA, 1999), 49--63, Progr. Probab., 47, Birkhäuser Boston, Boston, MA, 2000. MR1857314
  • Pinelis, Iosif. l'Hospital type rules for oscillation, with applications. JIPAM. J. Inequal. Pure Appl. Math. 2 (2001), no. 3, Article 33, 24 pp. (electronic). MR1876266
  • Pinelis, Iosif. L'Hospital type rules for monotonicity: applications to probability inequalities for sums of bounded random variables. JIPAM. J. Inequal. Pure Appl. Math. 3 (2002), no. 1, Article 7, 9 pp. (electronic). MR1888922
  • 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
  • Pinelis, Iosif. On inequalities for sums of bounded random variables. J. Math. Inequal. 2 (2008), no. 1, 1--7. MR2453629 http://arxiv.org/abs/math.PR/
  • Pinelis, Iosif. Toward the best constant factor for the Rademacher-Gaussian tail comparison. ESAIM Probab. Stat. 11 (2007), 412--426. MR2339301 http://arxiv.org/abs/
  • Pinelis, I. F.; Sakhanenko, A. I. Remarks on inequalities for probabilities of large deviations. (Russian) Teor. Veroyatnost. i Primenen. 30 (1985), no. 1, 127--131. MR0779438
  • Shorack, Galen R.; Wellner, Jon A. Empirical processes with applications to statistics. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. xxxviii+938 pp. ISBN: 0-471-86725-X MR0838963
  • Talagrand, Michel. Concentration of measure and isoperimetric inequalities in product spaces. Inst. Hautes Études Sci. Publ. Math. No. 81 (1995), 73--205. MR1361756
  • Whittle, P. Bounds for the moments of linear and quadratic forms in independent variables. Teor. Verojatnost. i Primenen. 5 1960 331--335. MR0133849
  • Jurinskiĭ, V. V. Exponential estimates for large deviations. (Russian) Teor. Verojatnost. i Primenen. 19 (1974), 152--154. MR0334298


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