대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권4호
  • /
  • Pages.771-778
  • /
  • 2006
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

STRONG LAWS FOR WEIGHTED SUMS OF I.I.D. RANDOM VARIABLES

  • Cai, Guang-Hui (Department of Mathematics and Statistics Zhejing Gongshang University)
  • 발행 : 2006.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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 ([12]).

키워드

참고문헌

  1. Z. D. Bai and P. E. Cheng, Marcinkiewicz strong laws for linear statistics, Statist. Probab. Lett. 46 (2000), 105-112 https://doi.org/10.1016/S0167-7152(99)00093-0
  2. B. D. Choi and S. H. Sung, Almost sure convergence theorems of weighted sums of random variables, Stochastic Anal. Appl. 5 (1987), 365-377 https://doi.org/10.1080/07362998708809124
  3. Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, Springer-Verlag, New York, 3rd ed. 1997
  4. J. Cuzick, A strong law for weighted sums of i.i.d. random variables, J. Theoret. Probab. 8 (1995), 625-641 https://doi.org/10.1007/BF02218047
  5. P. Erdos, On a theorem of Hsu-Robbins, Ann. Math. Statist. 20 (1949), 286-291 https://doi.org/10.1214/aoms/1177730037
  6. P. L. Hsu adn H. Robbins, Complete convergence and the law of larege numbers, Proc. Nat. Acad. Sci. (USA) 33 (1947), no. 2, 25-31
  7. D. K. Joag and F. Proschan, Negative associated of random variables with application, Ann. Statist. 11 (1983), 286-295 https://doi.org/10.1214/aos/1176346079
  8. V. V. Petrov, Limit theorems of probability theory sequences of independent random variables, Oxford, Oxford Science Publications, 1995
  9. Q. M. Shao, A comparison theorem on moment inequalities between Negatively associated and independent random variables, J. Theoreti. Probab. 13 (2000), 343-356 https://doi.org/10.1023/A:1007849609234
  10. W. Stout, Almost sure convergence, New York, Academic Press, 1974
  11. S. H. Sung, Strong laws for weighted sums of i.i.d. random variables, Statist. Probab. Lett. 52 (2001), 413-419 https://doi.org/10.1016/S0167-7152(01)00020-7
  12. S. H. Sung, Strong laws for weighted sums of i.i.d. random variables (II), Bull. Korean. Math. Soc. 39 (2002), no. 4, 607-615 https://doi.org/10.4134/BKMS.2002.39.4.607
  13. W. B. Wu, On the strong convergence of a weighted sums Statist., Probab. Lett. 44 (1999), 19-22 https://doi.org/10.1016/S0167-7152(98)00287-9

피인용 문헌

  1. On Complete Convergence for Weighted Sums ofρ*-Mixing Random Variables vol.2013, 2013, https://doi.org/10.1155/2013/947487