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.
Keywords
bootstrap, 3-D rotations, mean matrix, spatial average