Vol. 7, No. 6, 2014

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A median estimator for three-dimensional rotation data

Melissa Bingham and Zachary Fischer

Vol. 7 (2014), No. 6, 713–722

The median is a way of measuring the center of a set of data that is robust to outlying values. However, the concept of a median for three-dimensional rotation data has been largely nonexistent. Although there are already ways to measure the center of three-dimensional rotation data using the idea of a “mean rotation”, the median estimator developed here is shown to be less influenced by outlying data points. A simulation study that investigates scenarios under which the median is an improvement over the mean will be discussed. An application to a three-dimensional data set in the area of human motion will be considered.

directional statistics, rotations, median
Mathematical Subject Classification 2010
Primary: 62H11, 62P99
Received: 3 August 2012
Revised: 30 August 2013
Accepted: 13 September 2013
Published: 20 October 2014

Communicated by Michael Dorff
Melissa Bingham
Department of Mathematics
University of Wisconsin - La Crosse
1725 State Street
La Crosse, WI 54601
United States
Zachary Fischer
15800 W. Bluemound Road
Suite 100
Brookfield, WI 53005
United States