Abstract
We consider bootstrap methods for constructing confidence regions for the mean shape of objects specified by labelled landmarks in two dimensions. Two statistics are considered: a pivotal statistic, T, derived using matrix perturbation arguments; and a Hotelling-type statistic, H , based on partial Procrustes tangent projections of the observations. We give a rigorous proof, under weak conditions, that the null asymptotic distribution of T is χ 2 . Simulation results show that (i) the confidence region procedure obtained by bootstrapping each statistic is clearly superior to the corresponding ‘tabular’ procedure; and (ii) the pivotal T bootstrap confidence regions generally have smaller coverage error than the Hotelling bootstrap confidence regions, especially for distributions with low concentration.
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