%0 Report %1 mccullagh_structured_2006 %A McCullagh, P. %C Chicago, IL %D 2006 %K imported %T Structured covariance matrices in multivariate regression models %U http://www.stat.uchicago.edu/~pmcc/reports/similarity.pdf %X A similarity matrix is a covariance matrix generated by additive nested common factors having independent components. The set of such matrices is a structured subset of covariance matrices, closed under permutation and restriction, which makes it potentially useful as a sub-model for the joint dependence of several responses. It is also equal to the set of rooted trees. Some issues connected with parameter estimation and Bayesian model formulation for such structured sets and subsets are discussed. Although the set of similarity matrices has a rich algebraic structure, the fact that it is not a manifold leads to difficulties in computational work. Keywords: Commutative semi-group; Dissimilarity matrix; Exchangeable partition; Exchangeable sequence; Exchangeable tree; Infinite divisibility; Latent factor; Levy fragmentation; Markov fragmentation; Multidimensional scaling; Multivariate dependence; Natural transformation; Rooted tree; Similarity matrix; Unrooted tree

@techreport{mccullagh_structured_2006, abstract = {A similarity matrix is a covariance matrix generated by additive nested common factors having independent components. The set of such matrices is a structured subset of covariance matrices, closed under permutation and restriction, which makes it potentially useful as a sub-model for the joint dependence of several responses. It is also equal to the set of rooted trees. Some issues connected with parameter estimation and Bayesian model formulation for such structured sets and subsets are discussed. Although the set of similarity matrices has a rich algebraic structure, the fact that it is not a manifold leads to difficulties in computational work. Keywords: Commutative semi-group; Dissimilarity matrix; Exchangeable partition; Exchangeable sequence; Exchangeable tree; Infinite divisibility; Latent factor; Levy fragmentation; Markov fragmentation; Multidimensional scaling; Multivariate dependence; Natural transformation; Rooted tree; Similarity matrix; Unrooted tree}, added-at = {2017-01-09T13:57:26.000+0100}, address = {Chicago, IL}, author = {McCullagh, P.}, biburl = {https://www.bibsonomy.org/bibtex/21d0c7fa203cd90134aaafc0a3955b30b/yourwelcome}, institution = {Department of Statistics, University of Chicago}, interhash = {8cafa537b372a2de22d28e982fdf9304}, intrahash = {1d0c7fa203cd90134aaafc0a3955b30b}, keywords = {imported}, timestamp = {2017-01-09T14:01:11.000+0100}, title = {Structured covariance matrices in multivariate regression models}, url = {http://www.stat.uchicago.edu/~pmcc/reports/similarity.pdf}, urldate = {2012-07-28}, year = 2006 }