Limit theorems for the median deviation

Peter Hall; A. H. Welsh

doi:10.1007/BF02481078

Limit theorems for the median deviation

Peter Hall^*, A. H. Welsh

^*Corresponding author for this work

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

32 Citations (Scopus)

Abstract

In this paper, we obtain a strong law and central limit theorem for the median deviation under only very mild smoothness conditions on the underlying distribution. Under an additional condition implied by symmetry, we derive a weak Bahadur representation for the median deviation and establish the asymptotic equivalence of the median deviation and the semi-interquartile range.

Original language	English
Pages (from-to)	27-36
Number of pages	10
Journal	Annals of the Institute of Statistical Mathematics
Volume	37
Issue number	1
DOIs	https://doi.org/10.1007/BF02481078
Publication status	Published - Dec 1985

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title = "Limit theorems for the median deviation",

abstract = "In this paper, we obtain a strong law and central limit theorem for the median deviation under only very mild smoothness conditions on the underlying distribution. Under an additional condition implied by symmetry, we derive a weak Bahadur representation for the median deviation and establish the asymptotic equivalence of the median deviation and the semi-interquartile range.",

keywords = "Median deviation, quantiles, robust estimation, scale estimation",

author = "Peter Hall and Welsh, {A. H.}",

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AU - Welsh, A. H.

PY - 1985/12

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AB - In this paper, we obtain a strong law and central limit theorem for the median deviation under only very mild smoothness conditions on the underlying distribution. Under an additional condition implied by symmetry, we derive a weak Bahadur representation for the median deviation and establish the asymptotic equivalence of the median deviation and the semi-interquartile range.

KW - Median deviation

KW - quantiles

KW - robust estimation

KW - scale estimation

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JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 1

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Limit theorems for the median deviation

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