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A Multivariate CLT for Local Dependence withn-1/2 log nRate and Applications to Multivariate Graph Related Statistics

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  • Rinott, Yosef
  • Rotar, Vladimir

Abstract

This paper concerns the rate of convergence in the central limit theorem for certain local dependence structures. The main goal of the paper is to obtain estimates of the rate in the multidimensional case. Certain one-dimensional results are also improved by using some more flexible characteristics of dependence. Assuming the summands are bounded, we obtain rates close to those for independent variables. As an application we study the rate of the normal approximation of certain graph related statistics which arise in testing equality of several multivariate distributions

Suggested Citation

  • Rinott, Yosef & Rotar, Vladimir, 1996. "A Multivariate CLT for Local Dependence withn-1/2 log nRate and Applications to Multivariate Graph Related Statistics," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 333-350, February.
    • Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:333-350
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    Citations

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    Cited by:

    1. Kojevnikov, Denis & Marmer, Vadim & Song, Kyungchul, 2021. "Limit theorems for network dependent random variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 882-908.
    2. Hashimzade, Nigar & Majumdar, Mukul, 2002. "Survival under Uncertainty in an Exchange Economy," Working Papers 02-12, Cornell University, Center for Analytic Economics.
    3. M. Raič, 2004. "A Multivariate CLT for Decomposable Random Vectors with Finite Second Moments," Journal of Theoretical Probability, Springer, vol. 17(3), pages 573-603, July.
    4. Mukul Majumdar & Nigar Hashimzade, 2005. "Survival, Uncertainty, and Equilibrium Theory: An Exposition," Studies in Economic Theory, in: Alessandro Citanna & John Donaldson & Herakles Polemarchakis & Paolo Siconolfi & Stephan E. Spear (ed.), Essays in Dynamic General Equilibrium Theory, pages 107-128, Springer.
    5. Xiao Fang, 2016. "A Multivariate CLT for Bounded Decomposable Random Vectors with the Best Known Rate," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1510-1523, December.
    6. Martschink, Bastian, 2014. "Bounds on convergence for the empirical vector of the Curie–Weiss–Potts model with a non-zero external field vector," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 118-126.

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