Predictive distribution of regression vector and residual sum of squares for normal multiple regression model

Khan, Shahjahan (2004) Predictive distribution of regression vector and residual sum of squares for normal multiple regression model. Communications In Statistics: Theory and Methods, 33 (10). pp. 2423-2443. ISSN 0361-0926

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Abstract

This paper proposes predictive inference for the multiple regression model with independent normal errors. The distributions of the sample regression vector (SRV) and the residual sum of squares (RSS) for the model are derived by using invariant differentials. Also the predictive distributions of the future regression vector (FRV) and the future residual sum of squares (FRSS) for the future regression model are obtained. Conditional on the realized responses, the future regression vector is found to follow a multivariate Student-t distribution, and that of the residual sum of squares follows a scaled beta distribution. The new results have been applied to the market return and accounting rate data to illustrate its application.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright requirements of the publisher.
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:33
Last Modified: 02 Jul 2013 22:35
Uncontrolled Keywords: multiple regression model; regression vector; residual sum of squares; non-informative prior; future regression model; predictive inference; future regression vector; multivariate normal; student-t; beta and gamma distributions
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010499 Statistics not elsewhere classified
01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1081/STA-200031471
URI: http://eprints.usq.edu.au/id/eprint/1048

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