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


  • 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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:2:p:449-465
    DOI: 10.1016/

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    Cited by:

    1. 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;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 287-290, June.
    2. 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.


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