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On the central limit theorem for modulus trimmed sums

Author

Listed:
  • Bazarova, Alina
  • Berkes, István
  • Horváth, Lajos

Abstract

We prove a functional central limit theorem for modulus trimmed i.i.d. variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The proof is based on the weak convergence of a two-parameter process where one of the parameters is time and the second one is the fraction of truncation.

Suggested Citation

  • Bazarova, Alina & Berkes, István & Horváth, Lajos, 2014. "On the central limit theorem for modulus trimmed sums," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 61-67.
    • Handle: RePEc:eee:stapro:v:86:y:2014:i:c:p:61-67
    DOI: 10.1016/j.spl.2013.12.006
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    References listed on IDEAS

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    1. Berkes, István & Horváth, Lajos, 2012. "The central limit theorem for sums of trimmed variables with heavy tails," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 449-465.
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