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References

  1. Abramovich, Y. A.; Wickstead, A. W. Remarkable classes of unital AM-spaces. J. Math. Anal. Appl. 180 (1993), no. 2, 398--411. MR1251867 (95f:46035)
  2. Abramovich, Y. A.; Aliprantis, C. D. Problems in operator theory.Graduate Studies in Mathematics, 51. American Mathematical Society, Providence, RI, 2002. xii+386 pp. ISBN: 0-8218-2147-4 MR1921783 (2003h:47073)
  3. Aizenman, Michael; Germinet, François; Klein, Abel; Warzel, Simone. On Bernoulli decompositions for random variables, concentration bounds, and spectral localization. Probab. Theory Related Fields 143 (2009), no. 1-2, 219--238. MR2449128
  4. Bartlett, M. S. (1935). The effect of non-normality on the $t$ distribution. Proc. Camb. Phil. Soc. 31, 223--231.
  5. Bentkus, Vidmantas. On Hoeffding's inequalities. Ann. Probab. 32 (2004), no. 2, 1650--1673. MR2060313 (2005e:60041)
  6. Bentkus, V.; Juškevičius, T. Bounds for tail probabilities of martingales using skewness and kurtosis. Lith. Math. J. 48 (2008), no. 1, 30--37. MR2398168
  7. Cambanis, Stamatis; Simons, Gordon; Stout, William. Inequalities for $Ek(X,Y)$ when the marginals are fixed. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 36 (1976), no. 4, 285--294. MR0420778 (54 #8790)
  8. Eaton, Morris L. A note on symmetric Bernoulli random variables. Ann. Math. Statist. 41 1970 1223--1226. MR0268930 (42 #3827)
  9. Eaton, M.L. (1974). A probability inequality for linear combinations of bounded random variables. Ann. Statist. 2, 609--614.
  10. Eaton, M. L.; Efron, Bradley. Hotelling's $Tsp{2}$ test under symmetry conditions. J. Amer. Statist. Assoc. 65 1970 702--711. MR0269021 (42 #3918)
  11. Efron, Bradley. Student's $t$-test under symmetry conditions. J. Amer. Statist. Assoc. 64 1969 1278--1302. MR0251826 (40 #5053)
  12. Gangbo, Wilfrid. The Monge mass transfer problem and its applications. Monge Ampère equation: applications to geometry and optimization (Deerfield Beach, FL, 1997), 79--104, Contemp. Math., 226, Amer. Math. Soc., Providence, RI, 1999. MR1660743 (99k:49092)
  13. Hall, Peter. The bootstrap and Edgeworth expansion.Springer Series in Statistics. Springer-Verlag, New York, 1992. xiv+352 pp. ISBN: 0-387-97720-1 MR1145237 (93h:62029)
  14. Hall, Peter; Wang, Qiying. Exact convergence rate and leading term in central limit theorem for Student's $t$ statistic. Ann. Probab. 32 (2004), no. 2, 1419--1437. MR2060303 (2005e:62025)
  15. Hoaglin, D. C. (1985). Summarizing shape numerically: The $g$- and $h$-distributions. In Exploring Data Tables, Trends, and Shapes (D. C. Hoaglin, F. Mosteller and J. W. Tukey, eds.) 461--514. Wiley, New York.
  16. Hoeffding, W. (1940). Masstabinvariante korrelationstheorie. Schr. Math. Inst. Univ. Berlin. 5, 179--233.
  17. Hoeffding, Wassily. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 1963 13--30. MR0144363 (26 #1908)
  18. Hoeffding, Wassily. The collected works of Wassily Hoeffding.Edited and with a preface by N. I. Fisher and P. K. Sen.Springer Series in Statistics: Perspectives in Statistics. Springer-Verlag, New York, 1994. xvi+658 pp. ISBN: 0-387-94310-2 MR1307621 (96c:62003)
  19. Kafadar, Karen. John Tukey and robustness.Tribute to John W. Tukey. Statist. Sci. 18 (2003), no. 3, 319--331. MR2056573 (2005e:62005)
  20. Kallenberg, Olav. Foundations of modern probability.Second edition.Probability and its Applications (New York). Springer-Verlag, New York, 2002. xx+638 pp. ISBN: 0-387-95313-2 MR1876169 (2002m:60002)
  21. Logan, B. F.; Mallows, C. L.; Rice, S. O.; Shepp, L. A. Limit distributions of self-normalized sums. Ann. Probability 1 (1973), 788--809. MR0362449 (50 #14890)
  22. Oates, D. K. (1971). A non-compact Krein-Milman theorem. Pacific J. Math. 36, 781--785.
  23. Parthasarathy, K. R.; Ranga Rao, R.; Varadhan, S. R. S. On the category of indecomposable distributions on topological groups. Trans. Amer. Math. Soc. 102 1962 200--217. MR0153041 (27 #3010)
  24. Pinelis, Iosif. Extremal probabilistic problems and Hotelling's $Tsp 2$ test under a symmetry condition. Ann. Statist. 22 (1994), no. 1, 357--368. MR1272088 (95m:62115)
  25. 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 (2009a:60021)
  26. Pinelis, Iosif. On normal domination of (super)martingales. Electron. J. Probab. 11 (2006), no. 39, 1049--1070 (electronic). MR2268536 (2009d:60123)
  27. Pinelis, I. (2006). Student's $t$-test without symmetry conditions. arXiv:math/0606160v1 [math.ST], http://arxiv.org/abs/math/0606160.
  28. Pinelis, Iosif. Exact inequalities for sums of asymmetric random variables, with applications. Probab. Theory Related Fields 139 (2007), no. 3-4, 605--635. MR2322709 (2008f:60024)
  29. Rachev, Svetlozar T.; Rüschendorf, Ludger. Mass transportation problems. Vol. I.Theory.Probability and its Applications (New York). Springer-Verlag, New York, 1998. xxvi+508 pp. ISBN: 0-387-98350-3 MR1619170 (99k:28006)
  30. Ratcliffe, J. F. (1968). The effect on the $t$-distribution of non-normality in the sampled population. Appl. Statist.17, 42--48.
  31. Shao, Qi-Man. Self-normalized large deviations. Ann. Probab. 25 (1997), no. 1, 285--328. MR1428510 (98b:60056)
  32. Skorokhod, A. V. Studies in the theory of random processes.Translated from the Russian by Scripta Technica, Inc. Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965 viii+199 pp. MR0185620 (32 #3082b)
  33. Tchen, André H. Inequalities for distributions with given marginals. Ann. Probab. 8 (1980), no. 4, 814--827. MR0577318 (82f:60052)
  34. Tukey, J. W. (1948). Some elementary problems of importance to small sample practice. Human Biol. 20, 205--214.
  35. Tukey, John W. On the comparative anatomy of transformations. Ann. Math. Statist. 28 (1957), 602--632. MR0091546 (19,986d)


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