호남수학학술지 (Honam Mathematical Journal)

  • 제29권3호
  • /
  • Pages.367-375
  • /
  • 2007
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

EXPONENTIAL INEQUALITY AND ALMOST SURE CONVERGENCE FOR THE NEGATIVELY ASSOCIATED SEQUENCE

  • 투고 : 2007.05.23
  • 심사 : 2007.06.30
  • 발행 : 2007.09.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

For bounded negatively associated random variables we derive almost sure convergence and specify the associated rate of convergence by establishing exponential inequality.

키워드

참고문헌

  1. L. Devroye, Exponential inequalities in nonparametric estimation In: Roussas, C. (Ed.) Nonparametric Functional Estimation and Related Topics, Kluwer Academic Publishers, Dordrecht(1991), 31-44
  2. W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Stat. Asso. 58(1963), 13-30 https://doi.org/10.2307/2282952
  3. Joag-Dev and K. Proschan, F., Negative association random variables with application, Ann. Statist. 11 (1983) 286-295 https://doi.org/10.1214/aos/1176346079
  4. T.S. Kim. and M.H. Ko, Almost sure convergence for weighted sums negatively dependence random variables, J. Korean Math. 42(2005) 949-957 https://doi.org/10.4134/JKMS.2005.42.5.949
  5. P. Matula, A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett. 15(1992) 209-213 https://doi.org/10.1016/0167-7152(92)90191-7
  6. C.M. Newman, Asymptotic independence and limit theorems for positively and negatively dependent random variables, In: Tong.Y.L.(Ed.), Inequalities in Statistics and Probability. IMS, Hayward, CA,(1984) pp.127-140
  7. G. G. Roussas, Exponential probability inequalities with some applications In: Ferguson, T. S., Shaping, L. S., MacQueen, J. B. (Ed.) Statistics, Probability and Game Theory, IMS Lecture Notes-Monograph series, Hayward, CA. 30(1996) 303-309
  8. Q. M. Shao, A comparison theorem on maximum inequalities between negatively associated and independent random variables. J. Theor. Probab. 13(2000) 343-356 https://doi.org/10.1023/A:1007849609234
  9. Q. M. Shao and C. Su, On the law of the iterated logarithm for infinite dimensional Ornstein-Ohlenbeck process, Canad. J. Math. 45(1993), 159-175 https://doi.org/10.4153/CJM-1993-009-2

피인용 문헌

  1. Exponential inequalities and complete convergence for a LNQD sequence vol.39, pp.4, 2010, https://doi.org/10.1016/j.jkss.2010.01.002
  2. Exponential inequalities for N-demimartingales and negatively associated random variables vol.79, pp.19, 2009, https://doi.org/10.1016/j.spl.2009.06.013