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

33 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

Access to Document

10.1007/BF02481078

Cite this

@article{8b298dcb0cc54f4eb07c1e98796804b7,

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.\}",

year = "1985",

month = dec,

doi = "10.1007/BF02481078",

language = "English",

volume = "37",

pages = "27--36",

journal = "Annals of the Institute of Statistical Mathematics",

issn = "0020-3157",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Limit theorems for the median deviation

AU - Hall, Peter

AU - Welsh, A. H.

PY - 1985/12

Y1 - 1985/12

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/51249174321

U2 - 10.1007/BF02481078

DO - 10.1007/BF02481078

M3 - Article

AN - SCOPUS:51249174321

SN - 0020-3157

VL - 37

SP - 27

EP - 36

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 1

ER -

Limit theorems for the median deviation

Abstract

Access to Document

Other files and links

Fingerprint

Cite this