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Meandian: A Measure of Location Based on Signed Rank of Deviations

12 Pages Posted: 21 Feb 2012 Last revised: 6 Mar 2012

John R. Doyle

Cardiff University - Cardiff Business School

Date Written: February 15, 2012

Abstract

A measure of location is examined that places itself where the signed rank deviations are as close to zero as possible. A solution algorithm is sketched. The measure is robust to outliers. In three illustrative real data examples we find the measure is usually intermediate between mean and median, hence provisionally called meandian. It tracks the mean and median closely when there is little skew. It is closer to the mean when skewing is light, but closer to the median when skewing is heavy. The measure has good stability when assessed using bootstrap resampling. Its connections with Wilcoxon’s signed rank test and the Hodges-Lehmann estimator are pointed out. The meandian may be generalized in a variety of ways, and breakdown points for the simple and generalized meandians are tabulated.

Keywords: mean, median, measure of location, rank deviation

JEL Classification: C10, C13, C14

Suggested Citation

Doyle, John R., Meandian: A Measure of Location Based on Signed Rank of Deviations (February 15, 2012). Available at SSRN: https://ssrn.com/abstract=2005995 or http://dx.doi.org/10.2139/ssrn.2005995

John Doyle (Contact Author)

Cardiff University - Cardiff Business School ( email )

Aberconway Building
Colum Drive
Cardiff, CF10 3EU
United Kingdom

HOME PAGE: http://www.cardiff.ac.uk/carbs/faculty/doylejr/index.html

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