This paper explores the predictive inference of future response(s), conditional on a set of observed responses from various linear regression models with t-error assumptions using the Bayesian approach. The models considered are the multiple regression models with multivariate t-error and the multivariate simple as well as multiple regression models with matrix-T errors. Analyses reveal that the prediction distributions of a single future response, a set of future responses and a future responses matrix for the study models are a univariate, multivariate Student-t distributions and matrix-T distributions respectively with appropriate location, scale and shape parameters. The shape parameter of these distributions depends on the size of the observed responses and the dimension of the regression parameters, but free from the degrees of freedom of the error distributions. Results are consistent with those obtained under normal error assumptions by a range of statistical approaches such as the structural distribution, structural relations of the model and classical methods. This indicates not only the inference robustness of models, but also indicates that the Bayesian approach is competitive with other statistical methods in predictive inference. Some applications of the results are also discussed with practical illustrations.
|Number of pages||1|
|Publication status||Published - 2013|
|Event||ISBA Regional Meeting and International Workshop/Conference on Bayesian Theory and Applications (IWCBTA) - Banaras Hindu University, Varanasi, India|
Duration: 06 Jan 2013 → 10 Jan 2013
|Conference||ISBA Regional Meeting and International Workshop/Conference on Bayesian Theory and Applications (IWCBTA)|
|Period||06/01/13 → 10/01/13|