Statistical analysis on high-dimensional spheres and shape spaces

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dc.creatorDryden, Ian L.
dc.date2005-08-16
dc.date.accessioned2026-07-07T08:07:09Z
dc.date.available2026-07-07T08:07:09Z
dc.descriptionWe consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines. First the uniform measure on the infinite-dimensional sphere is reviewed, together with connections with Wiener measure. We then discuss densities of Gaussian measures with respect to Wiener measure. Some nonuniform distributions on infinite-dimensional spheres and shape spaces are introduced, and special cases which have important practical consequences are considered. We focus on the high-dimensional real and complex Bingham, uniform, von Mises-Fisher, Fisher-Bingham and the real and complex Watson distributions. Asymptotic distributions in the cases where dimension and sample size are large are discussed. Approximations for practical maximum likelihood based inference are considered, and in particular we discuss an application to brain shape modeling.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053605000000264 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0508279
dc.identifierhttp://arxiv.org/abs/math/0508279
dc.identifierAnnals of Statistics 2005, Vol. 33, No. 4, 1643-1665
dc.identifierdoi:10.1214/009053605000000264
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130844
dc.subjectStatistics Theory
dc.subject62H11, 60G15 (Primary)
dc.titleStatistical analysis on high-dimensional spheres and shape spaces
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