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

References

  1. Bentkus, V.; Bloznelis, M.; Gˆtze, F. A Berry-EssÈen bound for Student's statistic in the non-i.i.d. case. J. Theoret. Probab. 9 (1996), no. 3, 765--796. MR1400598 (97e:60036)
  2. Bentkus, V.; Gˆtze, F.. The Berry-Esseen bound for Student's statistic. Ann. Probab. 24 (1996), 491--503. MR1387647 (97f:62021)
  3. Bentkus, V.; Gˆtze, F.; van Zwet, W. R. An Edgeworth expansion for symmetric statistics. Ann. Statist. 25 (1997), no. 2, 851--896. MR1439326 (98k:62017)
  4. Chistyakov, G. P.; Gˆtze, F. Moderate deviations for Student's statistic. Teor. Veroyatnost. i Primenen. 47 (2003), no. 3, 415--428. MR1975426 (2004c:60140)
  5. Friedrich, Karl O. A Berry-Esseen bound for functions of independent random variables. Ann. Statist. 17 (1989), no. 1, 170--183. MR0981443 (90c:60015)
  6. GinÈ, Evarist; Gˆtze, Friedrich; Mason,David M. When is the Student $t$-statistic asymptotically standard normal? Ann. Probab. 25 (1997), no. 3, 1514--1531. MR1457629 (98j:60033)
  7. Hall, Peter. Edgeworth expansion for Student's $t$ statistic under minimal moment conditions. Ann. Probab. 15 (1987), no. 3, 920--931. MR0893906 (88j:62039)
  8. Hall, Peter. On the effect of random norming on the rate of convergence in the central limit theorem. Ann. Probab. 16 (1988), no. 3, 1265--1280. MR0942767 (89e:60043)
  9. Hall, Peter; Jing, Bing-Yi. Uniform coverage bounds for confidence intervals and Berry-Esseen theorems for Edgeworth expansion. Ann. Statist. 23 (1995), no. 2, 363--375. MR1332571 (96b:62077)
  10. He, Xuming; Shao, Qi-Man. On parameters of increasing dimensions. J. Multivariate Anal. 73 (2000), no. 1, 120--135. MR1766124 (2001g:62016)
  11. Jing, Bing-Yi; Shao, Qi-Man; Wang, Qiying. Self-normalized CramÈr-type large deviations for independent random variables. Ann. Probab. 31 (2003), no. 4, 2167--2215. MR2016616 (2004k:60069)
  12. 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)
  13. Petrov, Valentin V. Limit theorems of probability theory. Sequences of independent random variables. Oxford Studies in Probability, 4. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. MR1353441 (96h:60048)
  14. Prawitz, H.akan. Limits for a distribution, if the characteristic function is given in a finite domain. Skand. Aktuarietidskr. 1972, 138--154 (1973) MR0375429 (51 #11622)
  15. Putter, Hein; van Zwet, Willem R. Empirical Edgeworth expansions for symmetric statistics. Ann. Statist. 26 (1998), no. 4, 1540--1569. MR1647697 (99k:62036)
  16. Slavova, V. V. On the Berry-Esseen bound for Student's statistic. Stability problems for stochastic models (Uzhgorod, 1984), 355--390, Lecture Notes in Math., 1155, Springer, Berlin, 1985. MR0825335 (87i:60029)
  17. Shao, Qi-Man. A CramÈr type large deviation result for Student's $t$-statistic. J. Theoret. Probab. 12 (1999), no. 2, 385--398. MR1684750 (2000d:60046)
  18. van Zwet, W. R. A Berry-Esseen bound for symmetric statistics. Z. Wahrsch. Verw. Gebiete 66 (1984), no. 3, 425--440. MR0751580 (86h:60063)
  19. Wang, Qiying; Jing, Bing-Yi. An exponential nonuniform Berry-Esseen bound for self-normalized sums. Ann. Probab. 27 (1999), no. 4, 2068--2088. MR1742902 (2001c:60045)
  20. Wang, Qiying; Jing, Bing-Yi; Zhao, Lincheng. The Berry-Esseen bound for Studentized statistics. Ann. Probab. 28 (2000), no. 1, 511--535. MR1756015 (2001a:62011)


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