Far East Journal of Theoretical Statistics
Volume 24, Issue 1, Pages 35 - 48
(January 2008)
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PREDICTION DISTRIBUTION FOR LINEAR REGRESSION MODEL WITH MULTIVARIATE STUDENT-t ERRORS
Azizur Rahman (Australia) and Shahjahan Khan (Australia)
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Abstract: The
Bayesian approach under uniform prior is employed in this paper
to derive the prediction distribution for multiple regression model with
multivariate Student-t error distribution. Conditional on a set of realized responses, a
single and a set of future responses have a univariate and multivariate Student-t
distributions, respectively, whose degrees of freedom depend on the size of the
realized sample and the dimension of the regression parameters’ vector but do
not depend on the degrees of freedom of the error distribution. Results are
identical to those obtained under normal error distribution by a range of
statistical approaches such as the structural distribution, structural relations
and classical methods. This indicates not only the inference robustness with
respect to departures from normal error to multivariate Student-t
error distributions, but also indicates that the Bayesian approach with uniform
prior is competitive with other statistical methods in the derivation of
prediction distribution. |
Keywords and phrases: multiple
regression model, multivariate Student-t
errors, Bayesian method, uniform prior, prediction distribution, beta,
univariate and multivariate Student-t
distributions.
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Communicated by Andrew Rosalsky |
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