Bootstrap Confidence Region Estimation of the Motion of Rigid Bodies

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Abstract
This article deals with statistical inference of the motion of rigid bodies using bootstrap methodology. We consider two types of motion: motion in p dimensional Euclidean space, and motion on a p-dimensional sphere. This article is motivated by problems of interest to polar scientists understanding the motion of ice pack at the North Pole and those to geoscientists studying the motion of tectonic plates. In addition to obtaining the point estimates for various parameters describing the motion of rigid bodies, we also perform confidence region estimation and testing of certain hypotheses. We consider two types of situations: when homologous data are available, and when the data consists of nonhomologous points. We illustrate the methodology by analyzing two data sets: a data set on the motion of arctic sea ice, and a data set from plate tectonics.

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