Prediction distribution for linear regression model with multivariate student-t errors

Rahman, Azizur and Khan, Shahjahan (2008) Prediction distribution for linear regression model with multivariate student-t errors. Far East Journal of Theoretical Statistics, 24 (1). pp. 35-48. ISSN 0972-0863

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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Awaiting copyright advice.
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Jul 2008 01:34
Last Modified: 02 Jul 2013 23:03
Uncontrolled 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
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
13 Education > 1303 Specialist Studies in Education > 130303 Education Assessment and Evaluation
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/4210

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