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Multilinear forms and measures of dependence between random variables

Author

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  • Bradley, Richard C.
  • Bryc, Wlodzimierz

Abstract

Based on an idea of Rosenblatt, the methods of interpolation theory are used to establish moment inequalities and equivalence relations for measures of dependence between two or more families of random variables. A couple of "interpolation" theorems proved here appear to be new.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:16:y:1985:i:3:p:335-367
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    Citations

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    Cited by:

    1. Miller, Curtis, 1995. "A CLT for the periodograms of a [varrho]*-mixing random field," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 313-330, December.
    2. Picard, Frederic, 2007. "A multilinear form inequality," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 774-788, April.
    3. Peligrad, Magda, 2002. "Some remarks on coupling of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 201-209, November.
    4. Sun, Jiaming, 1997. "Exponential convergence for sequences of random variables," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 159-164, June.
    5. Bucchia, Béatrice & Wendler, Martin, 2017. "Change-point detection and bootstrap for Hilbert space valued random fields," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 344-368.
    6. Bradley, Richard C., 1996. "A covariance inequality under a two-part dependence assumption," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 287-293, November.
    7. Sergey Utev & Magda Peligrad, 2003. "Maximal Inequalities and an Invariance Principle for a Class of Weakly Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(1), pages 101-115, January.
    8. Manel Kacem & Stéphane Loisel & Véronique Maume-Deschamps, 2016. "Some mixing properties of conditionally independent processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1241-1259, March.
    9. Tyran-Kaminska, Marta, 2010. "Convergence to Lévy stable processes under some weak dependence conditions," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1629-1650, August.
    10. Bulinski, Alexander & Suquet, Charles, 2001. "Normal approximation for quasi-associated random fields," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 215-226, September.
    11. Bradley, Richard C., 1997. "Every "lower psi-mixing" Markov chain is "interlaced rho-mixing"," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 221-239, December.

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