Optimal tolerance regions for future regression vector and residual sum of squares of multiple regression model with multivariate spherically contoured errors
Article
Article Title | Optimal tolerance regions for future regression vector and residual sum of squares of multiple regression model with multivariate spherically contoured errors |
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ERA Journal ID | 857 |
Article Category | Article |
Authors | |
Author | Khan, Shahjahan |
Journal Title | Statistical Papers |
Journal Citation | 50 (3), pp. 511-525 |
Number of Pages | 15 |
Year | 2009 |
Place of Publication | Germany |
ISSN | 0932-5026 |
1613-9798 | |
Digital Object Identifier (DOI) | https://doi.org/10.1007/s00362-007-0095-y |
Web Address (URL) | http://www.springerlink.com/content/16r13k3k364v774t/fulltext.pdf |
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. |
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 |
ANZSRC Field of Research 2020 | 490599. Statistics not elsewhere classified |
490509. Statistical theory | |
Public Notes | 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 |
Byline Affiliations | Australian Centre for Sustainable Catchments |
https://research.usq.edu.au/item/9z023/optimal-tolerance-regions-for-future-regression-vector-and-residual-sum-of-squares-of-multiple-regression-model-with-multivariate-spherically-contoured-errors
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