A robust scale estimator based on pairwise means

Garth Tarr*, Samuel Müller, Neville Weber

*Corresponding author for this work

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We propose a new robust scale estimator, the pairwise mean scale estimator P n, which in its most basic form is the interquartile range of the pairwise means. The use of pairwise means leads to a surprisingly high efficiency across many distributions of practical interest. The properties of P n are presented under a unified generalised L-statistics framework, which encompasses numerous other scale estimators. Extensions to P n are proposed, including taking the range of the middle τ × 100% instead of just the middle 50% of the pairwise means as well as trimming and Winsorising both the original data and the pairwise means. Furthermore, we have implemented a method using adaptive trimming, which achieves a maximal breakdown value. We investigate the efficiency properties of the pairwise mean scale estimator relative to a number of other established robust scale estimators over a broad range of distributions using the corresponding maximum likelihood estimates as a common base for comparison.

Original languageEnglish
Pages (from-to)187-199
Number of pages13
JournalJournal of Nonparametric Statistics
Volume24
Issue number1
DOIs
Publication statusPublished - Mar 2012
Externally publishedYes

Keywords

  • robust statistics
  • generalised L-statistics
  • scale estimation
  • Hodges-Lehmann estimator
  • random trimming

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