TY - JOUR
T1 - Statistics of ambiguous rotations
AU - Arnold, R.
AU - Jupp, P. E.
AU - Schaeben, H.
PY - 2018/5
Y1 - 2018/5
N2 - The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous rotations arise in biomechanics, crystallography and seismology. We develop methods for analyzing data of this form. A test of uniformity is given. Parametric models for ambiguous rotations are presented, tests of location are considered, and a regression model is proposed. An example involving orientations of diopside crystals (which have symmetry of order 2) is used throughout to illustrate how our methods can be applied.
AB - The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous rotations arise in biomechanics, crystallography and seismology. We develop methods for analyzing data of this form. A test of uniformity is given. Parametric models for ambiguous rotations are presented, tests of location are considered, and a regression model is proposed. An example involving orientations of diopside crystals (which have symmetry of order 2) is used throughout to illustrate how our methods can be applied.
KW - Frame
KW - Orientation
KW - Regression
KW - Symmetric array
KW - Symmetry
KW - Test of location
KW - Test of uniformity
U2 - 10.1016/j.jmva.2017.10.007
DO - 10.1016/j.jmva.2017.10.007
M3 - Article
VL - 165
SP - 73
EP - 85
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
SN - 0047-259X
ER -