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Some remarks on coupling of dependent random variables

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  • Peligrad, Magda

Abstract

In this note we investigate the coupling of a dependent random vector with an independent one, having the same marginal distributions. An upper bound of the distance in L1 between the variables with the same rank is given in terms of mixing coefficients. We shall apply our coupling method to the uniform law of large numbers.

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  • Peligrad, Magda, 2002. "Some remarks on coupling of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 201-209, November.
    • Handle: RePEc:eee:stapro:v:60:y:2002:i:2:p:201-209
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    References listed on IDEAS

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    1. Bradley, Richard C. & Bryc, Wlodzimierz, 1985. "Multilinear forms and measures of dependence between random variables," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 335-367, June.
    2. Nobel, Andrew & Dembo, Amir, 1993. "A note on uniform laws of averages for dependent processes," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 169-172, June.
    3. Yukich, J. E., 1986. "Rates of convergence for classes of functions: The non-i.i.d. case," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 175-189, December.
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    Cited by:

    1. J. Dedecker & C. Prieur, 2004. "Coupling for τ-Dependent Sequences and Applications," Journal of Theoretical Probability, Springer, vol. 17(4), pages 861-885, October.
    2. Shashkin, Alexey, 2008. "A strong invariance principle for positively or negatively associated random fields," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2121-2129, October.

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