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The Strong Laws of Large Numbers for Weighted Averages of Dependent Random Variables

  • Kim, Tae-Sung (Division of Mathematics & Informational Statistics & Institute of Basic Natural Science Wonkwang University) ;
  • Lee, Il-Hyun (Division of Mathematics & Informational Statistics Wonkwang University) ;
  • Ko, Mi-Hwa (Division of Mathematics & Informational Statistics Wonkwang University)
  • Published : 2002.08.01

Abstract

We derive the strong laws of large numbers for weighted averages of partial sums of random variables which are either associated or negatively associated. Our theorems extend and generalize strong law of large numbers for weighted sums of associated and negatively associated random variables of Matula(1996; Probab. Math. Statist. 16) and some results in Birkel(1989; Statist. Probab. Lett. 7) and Matula (1992; Statist. Probab. Lett. 15 ).

Keywords

References

  1. Statistics & Probability Letters v.7 A note on the strong laws of large number for positively dependent random variables Birkel, T.
  2. Journal of Theoretical Probability v.9 The strong law of large number for weighted averages under dependence assumptions Chandra, K.;S. Ghosal https://doi.org/10.1007/BF02214087
  3. Statistics & Probability letters v.50 Maximal inequalities for demimartingales and a strong law of large numbers Christofides, T. C. https://doi.org/10.1016/S0167-7152(00)00116-4
  4. Annals of Mathematical Statistics v.38 Association of random variables with applications Esary, J.;F. Proschan;D. Walkup https://doi.org/10.1214/aoms/1177698701
  5. Annals of Statistics v.11 Negative association of random variables with applications Joag-Dev, K.;F. Proschan https://doi.org/10.1214/aos/1176346079
  6. Statistics & Probability Letters v.43 The Haject-Renyi inequality for the NA random variables and its application Liu, J.;Gan S.;Chen, P. https://doi.org/10.1016/S0167-7152(98)00251-X
  7. Statistics & Probability Letters v.15 A note on the almost sure convergence of sums of negatively dependent random variables Matula, P. https://doi.org/10.1016/0167-7152(92)90191-7
  8. Probability and Mathematical Statistics v.16 Convergence of weighted averages of associated random variables Matula, P.
  9. Probaility and Mathematical Statistics v.18 On the almost sure central limit theorem for associated random variables Matula, P.
  10. Inequalities in Statistics and Probability Asymptotic independence and limit theorems for positively and negatively dependent random variables Newman, C.M.;Y. L. Tong(ed.)
  11. Zeitshrift fur Wahrscheinlickkeits theorie und verwandte gebiete v.59 Associated random variables and martingale inequalities Newman, C. M.;A. L. Wright https://doi.org/10.1007/BF00532227