Optimal tolerance regions for future regression vector and residual sum of squares of multiple regression model with multivariate spherically contoured errors

Khan, Shahjahan ORCID: https://orcid.org/0000-0002-0446-086X (2009) Optimal tolerance regions for future regression vector and residual sum of squares of multiple regression model with multivariate spherically contoured errors. Statistical Papers, 50 (3). pp. 511-525. ISSN 0932-5026

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Abstract

This paper considers multiple regression model with multivariate spherically symmetric errors to determine optimal β-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. The prediction distribution of the FRV, conditional on the observed responses, is multivariate Student-t distribution. Similarly, the prediction distribution of the FRSS is a beta distribution. The optimal β-expectation tolerance regions for the FRV and FRSS have been obtained based on the F -distribution and beta distribution, respectively. The results in this paper are applicable for multiple regression model with normal and Student-t errors.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Accepted version deposited in accordance with the copyright policy of the publisher. Copyright 2009 Springer. This is It is posted here with permission of the publisher for your personal use. No further distribution is permitted. The original publication is available at: http://www.springerlink.com
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Faculty/School / Institute/Centre: Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013)
Date Deposited: 22 Jul 2009 11:01
Last Modified: 02 May 2017 06:08
Uncontrolled Keywords: multiple regression model; prediction distribution; optimal β; expectation tolerance region; invariant differential; non-informative prior; spherical/elliptical distributions; multivariate Student-t; beta and F-distributions
Fields of Research (2008): 01 Mathematical Sciences > 0104 Statistics > 010499 Statistics not elsewhere classified
01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: https://doi.org/10.1007/s00362-007-0095-y
URI: http://eprints.usq.edu.au/id/eprint/5184

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