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Exponential inequality for associated random variables

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  • Ioannides, D. A.
  • Roussas, G. G.

Abstract

Under mild conditions, a Bernstein-Hoeffding-type inequality is established for covariance invariant positively associated random variables. A condition is given for almost sure convergence, and the associated rate of convergence is specified in terms of the underlying covariance function.

Suggested Citation

  • Ioannides, D. A. & Roussas, G. G., 1999. "Exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 423-431, May.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:4:p:423-431
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    References listed on IDEAS

    as
    1. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    2. Roussas, G. G., 1994. "Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 152-173, July.
    3. Bagai, Isha & Prakasa Rao, B. L. S., 1991. "Estimation of the survival function for stationary associated processes," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 385-391, November.
    4. Cai, Zongwu & Roussas, George G., 1997. "Smooth estimate of quantiles under association," Statistics & Probability Letters, Elsevier, vol. 36(3), pages 275-287, December.
    5. Roussas, George G., 1995. "Asymptotic normality of a smooth estimate of a random field distribution function under association," Statistics & Probability Letters, Elsevier, vol. 24(1), pages 77-90, July.
    6. Roussas, George G., 1991. "Kernel estimates under association: strong uniform consistency," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 393-403, November.
    7. Isha Bagai & B. Prakasa Rao, 1995. "Kernel-type density and failure rate estimation for associated sequences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 253-266, June.
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    Cited by:

    1. Sung, Soo Hak, 2007. "A note on the exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1730-1736, December.
    2. Yang, Shanchao & Su, Chun & Yu, Keming, 2008. "A general method to the strong law of large numbers and its applications," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 794-803, April.
    3. Guodong Xing & Shanchao Yang, 2010. "Some Exponential Inequalities for Positively Associated Random Variables and Rates of Convergence of the Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 23(1), pages 169-192, March.

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