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An invariance principle for weakly associated random vectors

Author

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  • Burton, Robert M.
  • Dabrowski, AndréRobert
  • Dehling, Herold

Abstract

The positive dependence notion of association for collections of random variables is generalized to that of weak association for collections of vector valued random elements in such a way as to allow negative dependencies in individual random elements. An invariance principle is stated and proven for a stationary, weakly associated sequence of d-valued or separable Hilbert space valued random elements which satisfy a covariance summability condition.

Suggested Citation

  • Burton, Robert M. & Dabrowski, AndréRobert & Dehling, Herold, 1986. "An invariance principle for weakly associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 301-306, December.
    • Handle: RePEc:eee:spapps:v:23:y:1986:i:2:p:301-306
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    Citations

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    Cited by:

    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. R.M. Balan, 2003. "A Strong Invariance Principle for Associated Random Fields," RePAd Working Paper Series lrsp-TRS390, Département des sciences administratives, UQO.
    3. Antoine Lerbet, 2023. "Statistical inference on stationary shot noise random fields," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 551-580, October.
    4. Zhang, Li-Xin, 2001. "Strassen's law of the iterated logarithm for negatively associated random vectors," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 311-328, October.
    5. Vu T. N. Anh & Nguyen T. T. Hien & Le V. Thanh & Vo T. H. Van, 2021. "The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences," Journal of Theoretical Probability, Springer, vol. 34(1), pages 331-348, March.
    6. Kim, Tae-Sung & Ko, Mi-Hwa & Han, Kwang-Hee, 2008. "On the almost sure convergence for a linear process generated by negatively associated random variables in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2110-2115, October.
    7. Kim, Tae-Sung & Ko, Mi-Hwa, 2008. "A central limit theorem for the linear process generated by associated random variables in a Hilbert space," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2102-2109, October.
    8. Chen, Jia, 2008. "Asymptotics of kernel density estimators on weakly associated random fields," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3230-3237, December.
    9. Khoshnevisan, Davar & Lewis, Thomas M., 1998. "A law of the iterated logarithm for stable processes in random scenery," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 89-121, May.
    10. Xin Guo & Zhao Ruan & Lingjiong Zhu, 2015. "Dynamics of Order Positions and Related Queues in a Limit Order Book," Papers 1505.04810, arXiv.org, revised Oct 2015.
    11. Mi-Hwa Ko & Tae-Sung Kim & Kwang-Hee Han, 2009. "A Note on the Almost Sure Convergence for Dependent Random Variables in a Hilbert Space," Journal of Theoretical Probability, Springer, vol. 22(2), pages 506-513, June.
    12. Huang, Wen-Tao & Xu, Bing, 2002. "Some maximal inequalities and complete convergences of negatively associated random sequences," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 183-191, April.
    13. Thuan, Nguyen Tran & Quang, Nguyen Van, 2016. "Negative association and negative dependence for random upper semicontinuous functions, with applications," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 44-57.

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    Keywords

    invariance principle association;

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