| The multivariate t distribution has many potential applications in applied statistics. Current computational advances will make it routinely available in practice in the near future. This thesis concerns the computational aspects of the multivariate t distribution and consists of three topics.;First, we focus on maximum likelihood estimation of the parameters of the multivariate t, with known and unknown degrees of freedom, with and without missing data, and with and without covariates. We describe EM, ECM, and ECME algorithms for these cases and indicate their relative computational efficiencies. Maximum likelihood estimation is rarely the final answer when fitting t distributions to data, but it is nearly always an essential component of such endeavors.;Second, we focus on posterior simulation of the parameters of the multivariate t distribution in different cases: with known and unknown degrees of freedom, with and without missing data, and with and without covariates. When a rectangular multivariate data set contains missing values, the missing data imputation technique using the multivariate t distribution appears potentially useful. It can be used either to obtain robust estimates of the parameters of interest or to implement multiple imputation so that the filled-in multiple data sets allow for valid inferences. An efficient technique for implementation of the monotone missing data augmentation algorithm using the multivariate t distribution is obtained.;Third, we present the general framework of two future research topics: (1) extension of the general location model for mixed continuous and categorical data using the multivariate t distribution; and (2) hierarchical models and meta-analysis using the multivariate t distribution. |
