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The central limit theorem for sums of trimmed variables with heavy tails


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  • Berkes, István
  • Horváth, Lajos


Trimming is a standard method to decrease the effect of large sample elements in statistical procedures, used, e.g., for constructing robust estimators and tests. Trimming also provides a profound insight into the partial sum behavior of i.i.d. sequences. There is a wide and nearly complete asymptotic theory of trimming, with one remarkable gap: no satisfactory criteria for the central limit theorem for modulus trimmed sums have been found, except for symmetric random variables. In this paper we investigate this problem in the case when the variables are in the domain of attraction of a stable law. Our results show that for modulus trimmed sums the validity of the central limit theorem depends sensitively on the behavior of the tail ratio P(X>t)/P(|X|>t) of the underlying variable X as t→∞ and paradoxically, increasing the number of trimmed elements does not generally improve partial sum behavior.

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Bibliographic Info

Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 122 (2012)
Issue (Month): 2 ()
Pages: 449-465

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Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:449-465

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Keywords: Trimming; Heavy tails; Asymptotic normality; Domain of attraction; Nongaussian limit;


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Cited by:
  1. 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.
  2. Lajos Horváth & Gregory Rice, 2014. "Rejoinder on: Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 23(2), pages 287-290, June.


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