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On limiting distribution of U-statistics based on associated random variables

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  • Garg, Mansi
  • Dewan, Isha

Abstract

Let {Xn,n≥1} be a sequence of stationary associated random variables. We discuss another set of conditions under which a central limit theorem for U-statistics based on {Xn,n≥1} holds. We look at U-statistics based on differentiable kernels of degree 2 and above. As applications, we discuss consistent estimators of second, third and fourth central moments, and estimators of skewness and kurtosis based on them.

Suggested Citation

  • Garg, Mansi & Dewan, Isha, 2018. "On limiting distribution of U-statistics based on associated random variables," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 7-16.
    • Handle: RePEc:eee:stapro:v:132:y:2018:i:c:p:7-16
    DOI: 10.1016/j.spl.2017.08.016
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    References listed on IDEAS

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    1. Dewan, Isha & Prakasa Rao, B. L. S., 2002. "Central limit theorem for U-statistics of associated random variables," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 9-15, March.
    2. Christofides, Tasos C. & Vaggelatou, Eutichia, 2004. "A connection between supermodular ordering and positive/negative association," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 138-151, January.
    3. Garg, Mansi & Dewan, Isha, 2015. "On asymptotic behavior of U-statistics for associated random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 209-220.
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