Far East Journal of Theoretical Statistics
Volume 10, Issue 1, Pages 11 - 24
(May 2003)
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ROBUST PREDICTIVE INFERENCE FOR THE MULTIVARIATE LINEAR MODEL
B. M. Golam Kibria (U. S. A.)
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Abstract: This paper considers the predictive inference for the future
responses from the multivariate linear models with errors following an
elliptically contoured distribution. First we derive the marginal likelihood
function of unknown covariance parameters. Then we derive the predictive
distribution for known covariance parameters of the model. It is observed that
the predictive distribution of future responses of the model has a multivariate
Student’s t distribution, which is identical to that obtained under the
independently distributed multivariate normal errors and dependent but
uncorrelated t errors. This gives inference robustness with respect to
departures from the independent sampling from normal and dependent but
uncorrelated sampling from Student’s t to elliptically contoured
distribution. |
Keywords and phrases: elliptically contoured error, marginal likelihood, multivariate linear model,
predictive distribution, robustness, Student’s t distribution. |
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