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On the partial sums and extreme order statistics of i.i.d. random variables

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  • Ye, Jiacheng
  • Chen, Xin
  • Xiao, Jinghong

Abstract

This paper proves several limit theorems for the joint version of partial sums and extreme order statistics. The obtained results extend those of Li et al. (2024) to the case where the random variables have infinite variances.

Suggested Citation

  • Ye, Jiacheng & Chen, Xin & Xiao, Jinghong, 2025. "On the partial sums and extreme order statistics of i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 222(C).
    • Handle: RePEc:eee:stapro:v:222:y:2025:i:c:s0167715225000501
    DOI: 10.1016/j.spl.2025.110405
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    References listed on IDEAS

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    1. Csáki, Endre & Gonchigdanzan, Khurelbaatar, 2002. "Almost sure limit theorems for the maximum of stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 195-203, June.
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    4. Wu, Qunying, 2011. "Almost sure limit theorems for stable distributions," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 662-672, June.
    5. Aiping Hu & Zuoxiang Peng & Yongcheng Qi, 2009. "Joint behavior of point process of exceedances and partial sum from a Gaussian sequence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(3), pages 279-295, November.
    6. Tan, Zhongquan & Tang, Linjun, 2017. "On the maxima and sums of homogeneous Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 44-54.
    7. Zuoxiang Peng & Zhongquan Tan & Saralees Nadarajah, 2011. "Almost sure central limit theorem for the products of U-statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(1), pages 61-76, January.
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