A robust scale estimator based on pairwise means

Garth Tarr, Samuel Müller and Neville Weber

Journal of Nonparametric Statistics, 2012, vol. 24, issue 1, 187-199

Abstract: We propose a new robust scale estimator, the pairwise mean scale estimator Pn, 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 Pn are presented under a unified generalised L-statistics framework, which encompasses numerous other scale estimators. Extensions to Pn 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.

Date: 2012
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DOI: 10.1080/10485252.2011.621424

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