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Asymptotic distribution of the maximum interpoint distance for high-dimensional data

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  • Tang, Ping
  • Lu, Rongrong
  • Xie, Junshan

Abstract

Let X1,X2,…,Xn be a random sample coming from a p-dimensional population with independent sub-exponential components. Denote the maximum interpoint Euclidean distance by Mn=max1≤i

Suggested Citation

  • Tang, Ping & Lu, Rongrong & Xie, Junshan, 2022. "Asymptotic distribution of the maximum interpoint distance for high-dimensional data," Statistics & Probability Letters, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:stapro:v:190:y:2022:i:c:s0167715222001237
    DOI: 10.1016/j.spl.2022.109567
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    References listed on IDEAS

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    1. Henze, Norbert & Klein, Timo, 1996. "The Limit Distribution of the Largest Interpoint Distance from a Symmetric Kotz Sample," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 228-239, May.
    2. Tiefeng Jiang & Junshan Xie, 2020. "Limiting Behavior of Largest Entry of Random Tensor Constructed by High-Dimensional Data," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2380-2400, December.
    3. M. J. Appel & R. P. Russo, 2006. "Limiting Distributions for the Maximum of a Symmetric Function on a Random Point Set," Journal of Theoretical Probability, Springer, vol. 19(2), pages 365-375, June.
    4. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    5. Tiefeng Jiang & Yongcheng Qi, 2015. "Likelihood Ratio Tests for High-Dimensional Normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 988-1009, December.
    Full references (including those not matched with items on IDEAS)

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