dc.contributor.author Pigoli, Davide en dc.contributor.author Menafoglio, Alessandra en dc.contributor.author Secchi, Piercesare en dc.date.accessioned 2015-12-17T16:42:42Z dc.date.available 2015-12-17T16:42:42Z dc.date.issued 2015-12-25 en dc.identifier.citation Pigoli et al. Journal of Multivariate Analysis (2016) Vol. 145, pp. 117-131. doi:10.1016/j.jmva.2015.12.006 en dc.identifier.issn 0047-259X dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/253013 dc.description.abstract The statistical analysis of data belonging to Riemannian manifolds is becoming increasingly important in many applications, such as shape analysis, diffusion tensor imaging and the analysis of covariance matrices. In many cases, data are spatially distributed but it is not trivial to take into account spatial dependence in the analysis because of the non linear geometry of the manifold. This work proposes a solution to the problem of spatial prediction for manifold valued data, with a particular focus on the case of positive definite symmetric matrices. Under the hypothesis that the dispersion of the observations on the manifold is not too large, data can be projected on a suitably chosen tangent space, where an additive model can be used to describe the relationship between response variable and covariates. Thus, we generalize classical kriging prediction, dealing with the spatial dependence in this tangent space, where well established Euclidean methods can be used. The proposed kriging prediction is applied to the matrix field of covariances between temperature and precipitation in Quebec, Canada. dc.language English en dc.language.iso en en dc.publisher Elsevier dc.subject non Euclidean data en dc.subject residual kriging en dc.subject positive definite symmetric matrices en dc.title Kriging prediction for manifold-valued random fields en dc.type Article dc.description.version This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jmva.2015.12.006 en prism.endingPage 131 prism.publicationDate 2015 en prism.publicationName Journal of Multivariate Analysis en prism.startingPage 117 prism.volume 145 en rioxxterms.versionofrecord 10.1016/j.jmva.2015.12.006 en rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2015-12-25 en dc.contributor.orcid Pigoli, Davide [0000-0003-4591-4167] dc.identifier.eissn 1095-7243 rioxxterms.type Journal Article/Review en rioxxterms.freetoread.startdate 2016-12-25
﻿