Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 49, 2015 - Issue 1
145
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

A general result of the almost sure central limit theorem of uniform empirical process

Pages 98-103 | Received 01 Apr 2013, Accepted 22 Nov 2013, Published online: 10 Jan 2014

References

  • Brosamler GA. An almost everywhere central limit theorem. Math Proc Cambridge Philos Soc. 1988;104:561–574. doi: 10.1017/S0305004100065750
  • Schatte P. On strong versions of the central limit theorem. Math Nachr. 1988;137:249–256. doi: 10.1002/mana.19881370117
  • Fahrner I, Stadtmüller U. On almost sure max-limit theorems. Stat Probab Lett. 1998;37:229–236. doi: 10.1016/S0167-7152(97)00121-1
  • Cheng SH, Peng L, Qi YC. Almost sure convergence in extreme value theory. Math Nachr. 1998;190:43–50. doi: 10.1002/mana.19981900104
  • Csáki E, Gonchigdanzan K. Almost sure limit theorems for the maximum of stationary Gaussian sequences. Stat Probab Lett. 2002;58:195–203. doi: 10.1016/S0167-7152(02)00128-1
  • Chen SQ, Lin ZY. Almost sure max-limits for nonstationary Gaussian sequence. Stat Probab Lett. 2006;76:1175–1184. doi: 10.1016/j.spl.2005.12.018
  • Peligrad M, Shao QM. A note on the almost sure central limit theorem for weakly dependent random variables. Stat Probab Lett. 1995;22:131–136. doi: 10.1016/0167-7152(94)00059-H
  • Dudziński M. A note on the almost sure central limit theorem for some dependent random variables. Stat Probab Lett. 2003;61:31–40. doi: 10.1016/S0167-7152(02)00291-2
  • Peng ZX, Wang LL, Nadarajah S. Almost sure central limit theorem for partial sums and maxima. Math Nachr. 2009;282:632–636. doi: 10.1002/mana.200610760
  • Dudziński M. The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences. Stat Probab Lett. 2008;78:347–357. doi: 10.1016/j.spl.2007.07.007
  • Wu QY. An improved result in almost sure central limit theory for products of partial sums with stable distribution. Chin Ann Math B. 2012;33(6):919–930. doi: 10.1007/s11401-012-0742-z
  • Wu QY. Almost sure limit theorems for stable distributions. Stat Probab Lett. 2011;81;662–672. doi: 10.1016/j.spl.2011.02.003
  • Wu QY. Almost sure central limit theory for products of sums of partial sums. Stat Probab Lett. 2011;81:662–672. doi: 10.1016/j.spl.2011.02.003
  • Zhang Y. A noteon almost sure central limit theorem for uniform empirical processes. J Jilin Univ Sci. 2011;49:687–689 (in Chinese).
  • Hörmann S. An extension of almost sure central limit theory. Stat Probab Lett. 2006;76:191–202. doi: 10.1016/j.spl.2005.07.015
  • Lacey MT, Philipp W. A note on the almost sure central limit theorem. Stat Probab Lett. 1990;9:201–205. doi: 10.1016/0167-7152(90)90056-D
  • Lin ZY, Lu CR, Su ZG. Foundations of probability limit theory. Beijing: Higher Education Press; 1999 (in Chinese)
  • Berkes I, Csáki E. A universal result in almost sure central limit theory, Stoch Process Appl. 2001;94:105–134. doi: 10.1016/S0304-4149(01)00078-3
  • Kiefer J, Wolfowitz J. On the deviations of the empiric distribution function of vector chance variables. Trans Am Math Soc. 1958;87:173–186. doi: 10.1090/S0002-9947-1958-0099075-1
  • Billingsley P. Convergence of probability measures. New York: Wiley; 1968.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.