Optimal tolerance regions for some functions of multiple regression model with Student-t errors

Khan, Shahjahan (2006) Optimal tolerance regions for some functions of multiple regression model with Student-t errors. Journal of Statistics and Management Systems, 9 (3). pp. 699-715. ISSN 0972-0510

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Abstract

This paper considers the multiple regression model to determine optimal beta-expectation tolerance regions for the future regression vector (FRV) and future residual sum of squares (FRSS) by using the prediction distributions of some appropriate functions of future responses. It is assumed that the errors of the regression model follow a multivariate Student-t distribution with unknown shape parameter, nu. The prediction distribution of the FRV, conditional on the observed responses, is a multivariate Student-t distribution but its shape parameter does not depend on the unknown degrees of freedom of the Student-t model. Similarly, the prediction distribution of the FRSS is a beta distribution. The optimal beta- expectation tolerance regions for the FRV and FRSS have been obtained based on the F-distribution and beta distribution respectively.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Full text of paper available for subscribers to the journal at http://www.tarupublications.com/jsms/FullText/JSMS-2006/JSMS-9-3-2006/jsms159.pdf. Author's final manuscript version deposited with permission of publisher.
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:49
Last Modified: 02 Jul 2013 22:39
Uncontrolled Keywords: Multiple regression model, prediction distribution, tolerance region, invariant differential, non-informative prior multivariate Student-t, beta and $F$ distributions.
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
01 Mathematical Sciences > 0104 Statistics > 010401 Applied Statistics
URI: http://eprints.usq.edu.au/id/eprint/1703

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