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

*István Berkes* and
*Lajos Horvath*

*Stochastic Processes and their Applications*, 2012, vol. 122, issue 2, 449-465

**Abstract:**
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.

**Keywords:** Trimming; Heavy tails; Asymptotic normality; Domain of attraction; Nongaussian limit (search for similar items in EconPapers)

**Date:** 2012

**References:** View complete reference list from CitEc

**Citations:** View citations in EconPapers (2) Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0304414911002663

Full text for ScienceDirect subscribers only

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:2:p:449-465

**Ordering information:** This journal article can be ordered from

http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional

https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by *T. Mikosch*

More articles in Stochastic Processes and their Applications from Elsevier

Bibliographic data for series maintained by Dana Niculescu ().