Bootstrap techniques for measures of center for three-dimensional rotation data

Bootstrapping is a nonparametric statistical technique that can be used to estimate the sampling distribution of a statistic of interest. This paper focuses on implementation of bootstrapping in a new setting, where the data of interest are 3-dimensional rotations. Two measures of center, the mean rotation and spatial average, are considered, and bootstrap confidence regions for these measures are proposed. The developed techniques are then used in a materials science application, where precision is explored for measurements of crystal orientations obtained via electron backscatter diffraction.