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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


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

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 56 (1996)
Issue (Month): 2 (February)
Pages: 333-350

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Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:333-350

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Keywords: Stein's method random graphs multivariate statistics;


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Cited by:
  1. 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.
  2. Majumdar, Mukul & Hashimzade, Nigar, 2004. "Survival, Uncertainty, and Equilibrium Theory: An Exposition," Working Papers 04-03, Cornell University, Center for Analytic Economics.
  3. Hashimzade, Nigar & Majumdar, Mukul, 2002. "Survival under Uncertainty in an Exchange Economy," Working Papers 02-12, Cornell University, Center for Analytic Economics.


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