Summability methods and negatively associated random variables

Journal of Applied Probability

Volumn 41A, Issue , 2004, Pages 231-238

  Bingham, N H ^a   Nili Sani, H R ^a  

^a NONE

Author keywords

Negatively associated random variable; Negatively dependent random variable; Summability methods

Indexed keywords

EID: 32544439159     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1082552201     Document Type: Article

References (41)

1. Bingham, N. H. (1984a). On Valiron and circle convergence. Math. Z. 186, 273-286.
2. Bingham, N. H. (1984b). Tauberian theorems for summability methods of random-walk type. J. London Math. Soc. 30, 281-287.
3. Bingham, N. H. (1986a). Extensions of the strong law. In Analytic and Geometric Stochastics (Adv. Appl. Prob. Suppl.), ed. D. G. Kendall, Applied Probability Trust, Sheffield, pp. 27-36.
4. Bingham, N. H. (1986b). Summability methods and dependent strong laws. In Dependence inProbabilityandStatistics (Progr. Prob. Statist. 11), Birkhäuser, Boston, MA, pp. 291-300.
5. Bingham, N. H. (1988). Tauberian theorems for Jakimovski and Karamata-Stirling methods. Mathematika 35, 216-224.
6. Bingham, N. H. (1989). Moving averages. In Almost Everywhere Convergence, Academic Press, Boston, MA, pp. 131-144.
7. Bingham, N. H. and Goldie, C. M. (1988). Riesz means and self-neglecting functions. Math. Z. 199, 443-454.
8. Bingham, N. H. and Maejima, M. (1985). Summability methods and almost sure convergence. Z. Wahrscheinlich-keitsth. 68, 383-392.
9. Bingham, N. H. and Stadtmüller, U. (1990). Jakimovski methods and almost-sure convergence. In Disorder in Physical Systems, eds G. R. Grimmett and D. J. A. Welsh, Oxford University Press, pp. 5-18.
10. Bingham, N. H. and Tenenbaum, G. (1986). Riesz and Valiron means and fractional moments. Math. Proc. Camb. Phil. Soc. 99, 143-149.
11. Block, H. W., Savits, T. H. and Shaked, M. (1985). A concept of negative dependence using stochastic ordering. Statist. Prob. Lett. 3, 81-86.
12. Bozorgnia, A., Patterson, R. F. and Taylor, R. L. (1996). Limit theorems for negatively dependent random variables. In Proc. 1st World Congr. NonlinearAnalysts (Tampa, FL, August 1992), Vol. 2, ed. V. Lakshmikantham, de Gruyter, Berlin, pp. 1639-1650.
13. Chandra, T. K. and Ghosal, S. (1996a). Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables. Acta Math. Hungar. 71, 327-336.
14. Chandra, T. K. and Ghosal, S. (1996b). The strong law of large numbers for weighted average under dependence assumptions. J. Theoret. Prob. 9, 797-809.
15. Chandrasekharan, K. and Minakshisundaram, S. (1952). Typical Means. Oxford University Press.
16. Chow, Y. S. (1973). Delayed sums and Borel summability of independent identically distributed random variables. Bull. Inst. Math. Acad. Sinica 1, 207-220.
17. Chung, K.-L. (1974). A Course in Probability Theory, 2nd edn. Academic Press, New York.
18. Ebrahimi, N. and Ghosh, M. (1981). Multivariate negative dependence. Commun. Statist. Theory Meth. 10,307-337.
19. Feller, W. (1971). An Introduction to Probability Theory and ItsApplications, Vol 2, 2nd edn. John Wiley, NewYork.
20. Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and Its Application. Academic Press, New York.
21. Hardy, G. H. (1949). Divergent Series. Clarendon Press, Oxford.
22. Ibragimov, I. A. and Linnik, Yu. V. (1971). Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff, Groningen.
23. Jakimovski, A. (1959). A generalization of the Lototosky method. Michigan Math. J. 6, 277-229.
24. Joag-Dev, K. and Proschan, F. (1983). Negative association of random variables with applications. Ann. Statist. 11, 286-295.
25. Joe, H. (1997). Multivariate Models and Dependence Concepts (Monogr. Statist Appl. Prob. 73). Chapman and Hall, London.
26. Jogdeo, K. and Patil, G. P. (1975). Probability inequalities for certain multivariate discrete distributions. Sankhya B 37, 158-164.
27. Karlin, S. and Rinott, Y. (1980). Classes of orderings of measures andrelatedcorrelationinequalities. J. Multivariate. Anal. 10, 499-516.
28. Kiesel, R. (1997). Strong laws and summability for sequences of ^-mixing random variables in Banach spaces. Electron. Commun. Prob. 2, 27-41.
29. Kiesel, R. (1998). Strong laws and summability for ^-mixing sequences of random variables. J. Theoret. Prob. 11, 209-234.
30. Korevaar, J. (2004). A Century ofTauberian Theory. Springer, Berlin (to appear).
31. Lai, T. L. (1974). Summability methods for independent, identically distributed random variables. Proc. Amer. Math. Soc. 45, 253-261.
32. Lehmann, E. L. (1966). Some concepts of dependence. Ann. Math. Statist. 43, 1137-1153.
33. Liang, H.-Y., Chen, Z.-J. and Su, C. (2002). Convergence of Jamison-type weighted sums of pairwise negatively quadrant dependent random variables. Acta Math. Appl. Sinica 18, 161-168.
34. Matula, P. (1992). A note on the almost sure convergence of sums of negatively dependent random variables. Statist. Prob. Lett. 15, 209-213.
35. n\-transformation of A. Jakimovski. Bull. Res. Council Israel F10, 165-187.
36. Meyer-Konig, W. (1949). Untersuchungen uber einige verwandte Limitierungsverfahren. Math. Z. 52, 257-304.
37. Newman, C. M. (1984). Asymptotic independence and limit theorems for positively and negatively dependent random variables. In Inequalities in Statistics and Probability (IMS Lecture Notes Monogr. Ser. 5), ed. Y L. Tong, IMS, Hayward, CA, pp. 127-140.
38. Peligrad, M. (1985). Convergence rates of the strong law for stationary mixing sequences. Z. Wahrscheinlichkeitsth. 70, 307-314.
39. Peligrad, M. (1989). The r-quick version of the strong law for stationary r-mixing sequences. In Almost Everywhere Convergence, eds G. A. Edgar and L. Sucheston, Academic Press, Boston, MA, pp. 335-348.
40. Shao, Q.-M. (2000). A comparison theorem on moment inequalities between negatively associated and independent random variables. J. Theoret Prob. 13, 343-356.
41. Shao, Q.-M. and Su, C. (1999). The law of the iterated logarithm for negatively associated random variables. Stoch. Process. Appl. 83, 139-148.