The problem of estimation has been widely investigated with all different kinds of assumptions. This study focusses on the subjective Bayesian estimation of a location vector and characteristic matrix for the univariate and multivariate elliptical model as oppose to objective Bayesian estimation that has been thoroughly discussed (see Fang and Li (1999) amongst others). The prior distributions that will be assumed is the conjugate normal-inverse Wishart prior and also the normal-Wishart prior which has not yet been considered in literature. The posterior distributions, joint and marginal, as well as the Bayes estimators will be derived. The newly developed results are applied to the multivariate normal and multivariate t-distribution. For subjective Bayesian analysis the vector-spherical matrix elliptical model is also studied. / Dissertation (MSc)--University of Pretoria, 2012. / Statistics / MSc / Unrestricted

In the 1880s and early 1890s, the Prague mathematician Eduard Weyr published his important results in matrix theory. His works represented the only significant contribution to matrix theory by Czech mathematicians in many decades that followed. Although Eduard Weyr was one of the few European mathematicians acquainted with matrix theory and working in it at that time, his results did not gain recognition for about a century. Eduard Weyr discovered the Weyr characteristic, which is a dual sequence to the better known Segre characteristic, and also the so-called typical form. This canonical form of a matrix is nowadays called the Weyr canonical form. It is permutationally similar to the commonly used Jordan canonical form of the same matrix and it outperforms the Jordan canonical form in some mathematical situations. The Weyr canonical form has become much better known in the last few years and even a monograph dedicated to this topic was published in 2011.