The Annals of Probability

Limit laws of modulus trimmed sums

Philip S. Griffin and Fozia S. Qazi

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Abstract

Let $X,X_1,X_2,\ldots$ be a sequence of independent and identically distributed random variables. Let $ ^{(1)}X_n,\ldots,{^{(n)}X}_n$ be an arrangement of $X_1$, $X_2,\ldots,X_n $ in decreasing order of magnitude, and set ${^{(r_n)}S}_n= {}^{(r_{n}+1)}X_n+\cdots + {^{(n)}X}_{n}$. This is known as the modulus trimmed sum. We obtain a complete characterization of the class of limit laws of the normalized modulus trimmed sum when the underlying distribution is symmetric and $ r_n \to \infty$, $r_nn^{-1}\to 0$.

Article information

Source
Ann. Probab., Volume 30, Number 3 (2002), 1466-1485.

Dates
First available in Project Euclid: 20 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1029867133

Digital Object Identifier
doi:10.1214/aop/1029867133

Mathematical Reviews number (MathSciNet)
MR1920273

Zentralblatt MATH identifier
1015.60017

Subjects
Primary: 60F05: Central limit and other weak theorems

Keywords
Trimmed sum limit laws stable laws

Citation

Griffin, Philip S.; Qazi, Fozia S. Limit laws of modulus trimmed sums. Ann. Probab. 30 (2002), no. 3, 1466--1485. doi:10.1214/aop/1029867133. https://projecteuclid.org/euclid.aop/1029867133


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References

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  • Sy RACUSE, NEW YORK 13244-1150 E-MAIL: psgriffi@sy r.edu DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE ST. MARY'S COLLEGE OF MARy LAND ST. MARY'S CITY, MARy LAND 20686 E-MAIL: fsqazi@smcm.edu