Prediction distribution for linear regression model with multivariate student-t errors
Article
Article Title | Prediction distribution for linear regression model with multivariate student-t errors |
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ERA Journal ID | 883 |
Article Category | Article |
Authors | Rahman, Azizur (Author) and Khan, Shahjahan (Author) |
Journal Title | Far East Journal of Theoretical Statistics |
Journal Citation | 24 (1), pp. 35-48 |
Number of Pages | 14 |
Year | 2008 |
Place of Publication | Delhi, India |
ISSN | 0972-0863 |
Web Address (URL) | http://www.pphmj.com/abstract/3050.htm |
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 | multiple regression model; multivariate student-t errors; Bayesian method; uniform prior; prediction distribution; beta student-t distributions; uni-variate student-t distributions; multivariate student-t distributions |
ANZSRC Field of Research 2020 | 490510. Stochastic analysis and modelling |
490509. Statistical theory | |
390402. Education assessment and evaluation | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | Faculty of Sciences |
Department of Mathematics and Computing |
https://research.usq.edu.au/item/9yv42/prediction-distribution-for-linear-regression-model-with-multivariate-student-t-errors
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