Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES

  • BAEK, JONG-IL (Division of Math. & Informational Statistics Institute of Basic Natural Science Wonkwang University) ;
  • PARK, SUNG-TAE (Division of Business Administration Wonkwang University) ;
  • CHUNG, SUNG-MO (Division of Math. & Informational Statistics Institute of Basic Natural Science Wonkwang University) ;
  • SEO, HYE-YOUNG (Division of Math. & Informational Statistics Institute of Basic Natural Science Wonkwang University)
  • Published : 2005.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let ${X,\;X_n|n\;\geq\;1}$ be a sequence of identically negatively associated random variables under some conditions. We discuss strong laws of weighted sums for arrays of negatively associated random variables.

Keywords

References

  1. K. Alam and K. M. L. Saxena, Positive dependence in multivariate distributions, Comm. Statist. Theory Methods A10 (1981), 1183-1196
  2. J. I. Baek, T. S. Kim and H. Y. Liang, On the convergence of moving average processes under dependent conditions, Aust. N. Z. J. Stat. 45 (2003), no. 3, 331-342 https://doi.org/10.1111/1467-842X.00287
  3. Z. D. Bai and P. E. Cheng, Marcinkiewicz strong lawss for linear statistics, Statist. Probab. Lett. 46 (2000), 105-112 https://doi.org/10.1016/S0167-7152(99)00093-0
  4. Z. D. Bai, P. E. Cheng, and C. H. Zhang, An extension of the Hardy-Littlewood strong law, Statist. Sinica, 1997, 923-928
  5. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968
  6. H. W. Block, T. H. Savits, and M. Shaked, Some concepts of negative dependence, Ann. Probab. 10 (1982), 765-772 https://doi.org/10.1214/aop/1176993784
  7. P. E. Cheng, A note on strong convergence rates in nonparametric regression, Statist. Probab. Lett. 24 (1995), 357-364 https://doi.org/10.1016/0167-7152(94)00195-E
  8. 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
  9. T. C. Hu, F. Moricz, and R. L. Taylor, Strong laws of large numbers for arrays of rounuise independent random variables, Statistics Technical Report 27. University of Georgia, 1986
  10. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), 286-295 https://doi.org/10.1214/aos/1176346079
  11. H. Y. Liang and C. Su, Complete convergence for weighted sums of NA sequences, Statist. Probab. Lett. 45 (1999), 85-95 https://doi.org/10.1016/S0167-7152(99)00046-2
  12. H. Y. Liang, Complete convergence for weighted sums of negatively associated random variables, Statist. Probab. Lett. 48 (2000), 317-325 https://doi.org/10.1016/S0167-7152(00)00002-X
  13. P. Matula, A note on the almost sure convergence of sums of negatively dependences random variables, Statist. Probab. Lett. 15 (1992), 209-213 https://doi.org/10.1016/0167-7152(92)90191-7
  14. C. M. Newman and Y. L. Tong, Asymptotic independence and limit theorems for positively and negatively dependent random variables (IMS, Hayward, CA), 1984, 127-140
  15. G. G. Roussas, Asymptotic normality of random fields of positively or negatively associated processes, J. Multivariate Anal. 50 (1994), 152-173 https://doi.org/10.1006/jmva.1994.1039
  16. Q. M. Shao, A comparison theorem on moment inequalities between negatively associated and independent random variables, J. Theoret. Probab. 13 (2000), 343-356 https://doi.org/10.1023/A:1007849609234
  17. C. Su, L. C. Zhao, and Y. B. Wang, Moment inequalities and weak convergence for negatively associated sequences, Sci. China Ser. A 40 (1997), 172-182 https://doi.org/10.1007/BF02874436
  18. S. 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

Cited by

  1. Weighted sums of associated variables vol.41, pp.4, 2012, https://doi.org/10.1016/j.jkss.2012.04.001
  2. ON ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF LNQD RANDOM VARIABLES vol.34, pp.2, 2012, https://doi.org/10.5831/HMJ.2012.34.2.241
  3. A Note on Weighted Sums of Associated Random Variables vol.143, pp.1, 2014, https://doi.org/10.1007/s10474-014-0397-1