A median estimator for three-dimensional rotation data

Abstract

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.