Statistics of Estimated Rotations

本项目研究估计旋转的统计，特别侧重于构造板块重建中出现的问题。我们建议将我们以前关于球面回归的m估计量的工作调整到这种重建中出现的数据类型。我们也建议发展固定热点假设的统计检验方法。这个问题的一个组成部分将是开发使用轮廓数据的方法。我们建议继续对拟合的旋转进行样条拼接，并为拟合的路径建立一个置信带。最后，我们建议继续研究在使用不同类型的数据计算重建时出现的Behrens Fisher型问题。这个项目是研究估计旋转的统计性质。这类问题出现在球体和欧几里德空间中刚体运动的统计估计或未知坐标系的统计估计中。在这些潜在的应用中，这条研究路线在科学上最引人注目的应用是构造板块重建误差的统计测定。该提案将集中研究在构造背景下出现的问题类型。

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.