Khan, Shahjahan ORCID: https://orcid.org/0000-0002-0446-086X
(2006)
*Prediction distribution of future regression and residual sum of squares matrices for multivariate simple regression model with correlated normal responses.*
Journal of Applied Probability and Statistics, 1 (1).
pp. 15-30.
ISSN 1930-6792

## Abstract

This paper considers multivariate simple regression model under normally distributed errors, for both realized and future responses, with unknown regression parameters and

covariance matrix.

The prediction distributions of the future regression matrix (FRM) and future residual sum of squares matrix (FRSSM) for the future regression model are obtained. Conditional on the realized responses, the FRM follows a matrix T distribution whose shape parameter depends on the sample size and the dimension of the regression parameters in the model, and the FRSSM follows a scaled generalized beta distribution. The same results have been obtained by both the classical and Bayesian methods under uniform prior.

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Item Type: | Article (Commonwealth Reporting Category C) |
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Refereed: | Yes |

Item Status: | Live Archive |

Additional Information: | Published version supplied by and deposited with blanket permission of publisher. Full text reference: Khan, S. (2006). Prediction distribution of future regression and residual sum of squares matrices for multivariate simple regression model with correlated normal responses, Journal of Applied Probability and Statistics, Vol. 1, 15-30. |

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: | 11 Oct 2007 01:11 |

Last Modified: | 02 Jul 2013 22:45 |

Uncontrolled Keywords: | multivariate simple regression model; invariant differentials; uniform prior; predictive inference; future regression matrix; residual sum of squares matrix; matrix normal; matrix T; generalized beta distributions |

Fields of Research (2008): | 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 |

URI: | http://eprints.usq.edu.au/id/eprint/2651 |

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