Remote Access Electronic Research Announcements

Electronic Research Announcements

ISSN 1079-6762



Strong laws for weighted sums of i.i.d. random variables

Author: Guang-hui Cai
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 29-36
MSC (2000): Primary 60F15
Published electronically: March 6, 2006
MathSciNet review: 2218628
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong laws under certain moment conditions on both the weights and the distribution. The result obtained extends and sharpens the result of Sung.

References [Enhancements On Off] (What's this?)

  • 1. Bai, Z. D. and Cheng, P. E., Marcinkiewicz strong laws for linear statistics, Statist. Probab. Lett. 46 (2000), 105-112. MR 1748864 (2001b:60043)
  • 2. Choi, B. D. and Sung, S. H., Almost sure convergence theorems of weighted sums of random variables, Stochastic Anal. Appl. 5 (1987), 365-377. MR 0912863 (88m:60079)
  • 3. Chow, Y. S. and Teicher, H., Probability Theory: Independence, Interchangeability, Martingales, Springer-Verlag, New York, 3rd ed., 1997. MR 1476912 (98e:60003)
  • 4. Cuzick, J., A strong law for weighted sums of i.i.d. random variables, J. Theoret. Probab. 8 (1997), 625-641. MR 1340830 (96f:60050)
  • 5. Erdös, P., On a theorem of Hsu-Robbins, Ann. Math. Statist. 20 (1949), 286-291. MR 0030714 (11,40f)
  • 6. Hsu, P. L. and Robbins, H., Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. (USA) 33 (1947), 25-31. MR 0019852 (8,470e)
  • 7. Petrov, V. V., Limit theorems of probability theory sequences of independent random variables, Oxford, Oxford Science Publications, 1995. MR 1353441 (96h:60048)
  • 8. Stout, W., Almost sure convergence, New York, Academic Press, 1974. MR 0455094 (56 #13334)
  • 9. Sung, S. H., Strong laws for weighted sums of i.i.d. random variables, Statist. Probab. Lett. 52 (2001), 413-419. MR 1841609 (2002f:60054)
  • 10. Wu, W. B., On the strong convergence of a weighted sum, Statist. Probab. Lett. 44 (1999), 19-22. MR 1706378 (2000d:60057)

Similar Articles

Retrieve articles in Electronic Research Announcements of the American Mathematical Society with MSC (2000): 60F15

Retrieve articles in all journals with MSC (2000): 60F15

Additional Information

Guang-hui Cai
Affiliation: Department of Mathematics and Statistics, Zhejiang Gongshang University, Hangzhou 310035, P. R. China

Keywords: Almost sure convergence, Marcinkiewicz-Zygmund strong laws
Received by editor(s): February 24, 2005
Published electronically: March 6, 2006
Additional Notes: The author would like to thank an anonymous referee for his/her valuable comments.
Communicated by: Mark Freidlin
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society