Bootstrap inference for mean reflection shape and size-and-shape with three-dimensional landmark data

摘要

Working within the framework of a multi-dimensional scaling approach to shape analysis, wendevelop bootstrap methods for inference about mean reflection shape and size-and-shape basednon labelled landmark data. The approach is developed in general dimensions though we focus onnthe three-dimensional case. We consider two pivotal statistics which we use to construct bootstrapnconfidence regions for the mean reflection shape or size-and-shape, and present simulationnresults which show that these statistics perform well in a variety of examples. We also suggestnregularized versions of the test statistics that are suitable for more challenging caseswhere samplensize is not sufficiently large in relation to the number of landmarks and present numerical resultsnconfirming that regularization indeed leads to better performance. An algorithm for producing angraphical representation of the confidence region for the mean reflection shape is presented andnapplied in an example involving molecular dynamics simulation data.