The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions
B.M.G. Kibria and S. Nadarajah (2006). The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions. Journal of Statistical Research, Vol. 40, No. 1, pp. 35-43.
This paper considers the heteroscedastic multivariate linear model with errors following elliptically contoured distributions. The marginal likelihood function of the unknown covariance parameters and the predictive distribution of future responses have been derived. The predictive distribution obtained is a product of m multivariate Student’s t distributions. It is interesting to note that when the models are assumed to have elliptically contoured distributions the marginal likelihood function of the parameters as well as the predictive distribution are identical to those obtained under independently distributed normal errors or dependent but uncorrelated Student’s t errors. Therefore, the distribution of future responses is unaffected by a change in the error distribution from the multivariate normal and multivariate t distributions to elliptically contoured distributions. This gives inference robustness with respect to departure from the reference case of independent sampling from the multivariate normal or dependent but uncorrelated sampling from multivariate t distributions to elliptically contoured distributions
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