Date of Award


Degree Type


Degree Name

Doctor of Philosophy


The prediction distributions of the future responses, conditional on the observed responses, from the multilinear models with multivariate Student-t and matrix-T errors are derived. These distributions provide the basis for the inference about the future responses. The cases of (i) dependent but uncorrelated and (ii) dependent and correlated responses are considered. The distribution of the Wishart matrix, and the prediction distribution of the regression and Wishart matrices have also been obtained for the generalized multilinear model with matrix-T errors.;For the multilinear models with first order auto-correlation, the marginal likelihood function of the auto-correlation coefficient has been obtained and used for the derivation of the prediction distributions. A simulation study has been conducted to illustrate the results.;As an application of the prediction distribution, the {dollar}\beta{dollar}-expectation tolerance regions are obtained for multilinear models by using the prediction distributions. First, a general procedure has been developed for the {dollar}\beta{dollar}-expectation tolerance region based on dependent responses under the framework of a structural model. Then it has been applied for the construction of the {dollar}\beta{dollar}-expectation tolerance regions for different multilinear models.;Structural inference procedure for the parameters of heteroscedastic simultaneous equation model has also been proposed for the general error distribution. The general results are then applied to the case of the multivariate normal and multivariate Student-t errors. The prediction distribution for the linear combinations of the future responses is also derived for the multivariate Student-t error.



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