The Annals of Probability

Asymptotic Normality of Trimmed Means in Higher Dimensions

R. A. Maller

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Abstract

A representation for the distribution of the trimmed sum of vector-valued random variables is obtained, generalising a one-dimensional formula. The trimming is with respect to observations falling outside a fixed family of sets, e.g., spheres. Asymptotic normality of the heavily trimmed sum, when normed and centered in different ways, is proved, and rates of convergence are given for some cases.

Article information

Source
Ann. Probab., Volume 16, Number 4 (1988), 1608-1622.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991587

Digital Object Identifier
doi:10.1214/aop/1176991587

Mathematical Reviews number (MathSciNet)
MR958206

Zentralblatt MATH identifier
0656.62022

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62H10: Distribution of statistics

Keywords
Trimmed means trimmed sums asymptotic normality rates of convergence

Citation

Maller, R. A. Asymptotic Normality of Trimmed Means in Higher Dimensions. Ann. Probab. 16 (1988), no. 4, 1608--1622. doi:10.1214/aop/1176991587. https://projecteuclid.org/euclid.aop/1176991587


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