Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY ORTHANT DEPENDENT RANDOM VARIABLES

  • Ko, MI-HwA (Statistical Research Center For Complex System) ;
  • KIM, TAE-SUNG (Department of Mathematics and Institute of Basic Science WonKwang University)
  • Published : 2005.09.01
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Abstract

For weighted sum of a sequence {X, X$\_{n}$, n $\geq$ 1} of identically distributed, negatively orthant dependent random variables such that |r| > 0, has a finite moment generating function, a strong law of large numbers is established.

Keywords

References

  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. T. K. Chandra and S. Ghosal, Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent random variables, Acta. Math. Hun- gar. 71 (1996), 327-336 https://doi.org/10.1007/BF00114421
  3. R. Cheng and S. Gan, Almost sure convergence of weighted sums of NA sequences, Wuhan Univ. J. Nat. Sci. 3 (1998), 11-16 https://doi.org/10.1007/BF02827504
  4. Y. S. Chow and T. L. Lai, Limiting behavior of weighted sums of independent random variables, Ann. Probab. 1 (1973), 810-824 https://doi.org/10.1214/aop/1176996847
  5. 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
  6. N. Ebrahimi and M. Ghosh, Multivariate Negative Dependence, Comm. Statist. Theory Methods 10 (1981), 307-336 https://doi.org/10.1080/03610928108828041
  7. E. L. Lehmann, Some Concepts of Dependence, Ann. Statist. 43 (1966), 1137- 1153
  8. 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
  9. Y. Qi, Limit theorems for sums and maxima of pairwise negative quadrant depen- dent random variables Syst. Sci. Math. Sci. 8 (1995), 251-253
  10. W. F. Stout, Almost Sure Convergence, Academic Press, New York, 1974
  11. H. Teicher, Almost certain convergence in double arrays, Z. Wahrsch. Verw. Gebiete 69 (1985), 331-345 https://doi.org/10.1007/BF00532738

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  2. Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Negatively Dependent Random Variables vol.2012, 2012, https://doi.org/10.1155/2012/425969
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  6. Weighted sums of associated variables vol.41, pp.4, 2012, https://doi.org/10.1016/j.jkss.2012.04.001
  7. Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables vol.39, pp.2, 2010, https://doi.org/10.1016/j.jkss.2009.05.003
  8. On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables vol.107, pp.2, 2013, https://doi.org/10.1007/s13398-012-0067-5
  9. A Note on Weighted Sums of Associated Random Variables vol.143, pp.1, 2014, https://doi.org/10.1007/s10474-014-0397-1
  10. An exponential inequality for a NOD sequence and a strong law of large numbers vol.24, pp.2, 2011, https://doi.org/10.1016/j.aml.2010.09.007
  11. Limiting behaviour for arrays of row-wise END random variables under conditions ofh-integrability vol.87, pp.3, 2015, https://doi.org/10.1080/17442508.2014.959951
  12. On the convergence rate for arrays of row-wise NOD random variables vol.45, pp.5, 2016, https://doi.org/10.1080/03610926.2013.786784
  13. Exponential inequality for a class of NOD random variables and its application vol.16, pp.1, 2011, https://doi.org/10.1007/s11859-011-0702-6
  14. EXPONENTIAL INEQUALITY AND ALMOST SURE CONVERGENCE FOR THE NEGATIVELY ASSOCIATED SEQUENCE vol.29, pp.3, 2007, https://doi.org/10.5831/HMJ.2007.29.3.367
  15. The Strong Consistency of the Estimator of Fixed-Design Regression Model under Negatively Dependent Sequences vol.2013, 2013, https://doi.org/10.1155/2013/521618
  16. Complete moment convergence for maximal partial sums under NOD setup vol.2015, pp.1, 2015, https://doi.org/10.1186/s13660-015-0577-8
  17. CONVERGENCE PROPERTIES OF THE PARTIAL SUMS FOR SEQUENCES OF END RANDOM VARIABLES vol.49, pp.6, 2012, https://doi.org/10.4134/JKMS.2012.49.6.1097
  18. Some Limit Theorems for Weighted Sums of Arrays of Nod Random Variables vol.32, pp.6, 2012, https://doi.org/10.1016/S0252-9602(12)60187-8
  19. On the strong convergence properties for weighted sums of negatively orthant dependent random variables vol.33, pp.1, 2018, https://doi.org/10.1007/s11766-018-3423-1
  20. Complete convergence for negatively orthant dependent random variables vol.2014, pp.1, 2014, https://doi.org/10.1186/1029-242X-2014-145