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A Multivariate CLT for Decomposable Random Vectors with Finite Second Moments

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  • M. Raič

    (University of Ljubljana)

Abstract

Stein's method is used to derive a CLT for dependent random vectors possessing the dependence structure from Barbour et al. J. Combin. Theory Ser. B 47, 125–145, but under the assumption of second moments only. This allows us to derive Lindeberg–Feller type theorems for sums of random vectors with certain dependence structures. We apply the main theorem to the study of three problems: local dependence, random graph degree statistics and finite population statistics. In particular, we consider U-statistics of independent observations as well as of observations drawn without replacement.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:17:y:2004:i:3:d:10.1023_b:jotp.0000040290.44087.68
    DOI: 10.1023/B:JOTP.0000040290.44087.68
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    References listed on IDEAS

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    1. 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.
    2. Dinh Pham & Joachim Möcks & Lothar Sroka, 1989. "Asymptotic normality of double-indexed linear permutation statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 415-427, September.
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    Cited by:

    1. Robert E. Gaunt, 2016. "Rates of Convergence in Normal Approximation Under Moment Conditions Via New Bounds on Solutions of the Stein Equation," Journal of Theoretical Probability, Springer, vol. 29(1), pages 231-247, March.
    2. 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.

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