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The limit theorem for maximum of partial sums of exchangeable random variables

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  • Alonso Ruiz, Patricia
  • Rakitko, Alexander

Abstract

We obtain the analogue of the classical result by Erdös and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central limit theorem of Blum et al. hold, the limit coincides with the classical one. Under more general assumptions, the probability of the random variables having conditional negative drift appears in the limit.

Suggested Citation

  • Alonso Ruiz, Patricia & Rakitko, Alexander, 2016. "The limit theorem for maximum of partial sums of exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 357-362.
    • Handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:357-362
    DOI: 10.1016/j.spl.2016.09.010
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    References listed on IDEAS

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    1. Berti, Patrizia & Rigo, Pietro, 1997. "A Glivenko-Cantelli theorem for exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 385-391, April.
    2. B. Prakasa Rao, 2009. "Conditional independence, conditional mixing and conditional association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 441-460, June.
    3. Gerardi, Anna & Spizzichino, Fabio & Torti, Barbara, 2000. "Exchangeable mixture models for lifetimes: the role of "occupation numbers"," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 365-375, October.
    4. Yu, Chang & Zelterman, Daniel, 2008. "Sums of exchangeable Bernoulli random variables for family and litter frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1636-1649, January.
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