Limit laws of modulus trimmed sums

Philip S. Griffin; Fozia S. Qazi

doi:10.1214/aop/1029867133

Limit laws of modulus trimmed sums

Philip S. Griffin, Fozia S. Qazi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let X, X₁, X₂,... be a sequence of independent and identically distributed random variables. Let ⁽¹⁾X_n,...,⁽ⁿ⁾X_n be an arrangement of X₁, X₂,...,X_n in decreasing order of magnitude, and set ^(rn)S_n = ^(rn+1)X_n +···+⁽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 → ∞, r_nn^-1 → 0.

Original language	English (US)
Pages (from-to)	1466-1485
Number of pages	20
Journal	Annals of Probability
Volume	30
Issue number	3
DOIs	https://doi.org/10.1214/aop/1029867133
State	Published - Jul 2002

Keywords

Limit laws
Stable laws
Trimmed sum

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/aop/1029867133

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abstract = "Let X, X1, X2,... be a sequence of independent and identically distributed random variables. Let (1)Xn,...,(n)Xn be an arrangement of X1, X2,...,Xn in decreasing order of magnitude, and set (rn)Sn = (rn+1)Xn +···+(n)Xn. 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 rn → ∞, rnn-1 → 0.",

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AU - Qazi, Fozia S.

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N2 - Let X, X1, X2,... be a sequence of independent and identically distributed random variables. Let (1)Xn,...,(n)Xn be an arrangement of X1, X2,...,Xn in decreasing order of magnitude, and set (rn)Sn = (rn+1)Xn +···+(n)Xn. 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 rn → ∞, rnn-1 → 0.

AB - Let X, X1, X2,... be a sequence of independent and identically distributed random variables. Let (1)Xn,...,(n)Xn be an arrangement of X1, X2,...,Xn in decreasing order of magnitude, and set (rn)Sn = (rn+1)Xn +···+(n)Xn. 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 rn → ∞, rnn-1 → 0.

KW - Limit laws

KW - Stable laws

KW - Trimmed sum

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JO - Annals of Probability

JF - Annals of Probability

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ER -

Limit laws of modulus trimmed sums

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Keywords

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