This project studies the statistics of estimated rotations with especial concentration on problems which arise in the reconstructions of tectonic plates. We propose to adapt our previous work on M-estimators for spherical regressions to the types of data which arise in such reconstructions. We also propose to develop methodology for a statistical test of the fixed hot spot hypothesis. One component of this problem will be to develop methodology for use with contoured data. We propose to continue our work on splining together fitted rotations and developing a confidence band for the fitted path. Finally, we propose to continue our work on Behrens Fisher type problems which arise when data of different types are used to calculate a reconstruction. This project is to study the statistical properties of estimated rotations. Such problems arise in the statistical estimation of the motion of rigid bodies on the sphere and in Euclidean space or in the statistical estimation of an unknown coordinate system. Of these potential applications, the most scientifically compelling application of this line of research is the statistical determination of the errors in tectonic plate reconstructions. The proposal will concentrate on studying the types of problems which arise in the tectonic context.
