Distribution of future location vector and residual sum of squares for multivariate location-scale model with spherically contoured errors

Khan, Shahjahan ORCID: https://orcid.org/0000-0002-0446-086X and Kabir, Md Enamul (2006) Distribution of future location vector and residual sum of squares for multivariate location-scale model with spherically contoured errors. Journal of Statistical Theory and Applications, 5 (2). pp. 91-104. ISSN 1538-7887

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Abstract

The multivariate location-scale model with a family of
spherically contoured errors is considered for both realized and
future responses.
The predictive distributions of the
future location vector (FLV) and future residual sum of squares
(FRSS) for the future responses are obtained. Conditional on the
realized responses, the FLV follows a multivariate Student-t
distribution whose shape parameter depends on the sample size and
the dimension of the location parameters of the model, and the
FRSS follows a scaled beta distribution. The results obtained by
both the classical and Bayesian methods under uniform prior are
identical. This paper generalizes the results for location-scale
models with multivariate normal and Student-t models to a wider
family of spherically/ellipticcally contoured models.

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Item Type:	Article (Commonwealth Reporting Category C)
Refereed:	Yes
Item Status:	Live Archive
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 00:33
Last Modified:	02 Jul 2013 22:35
Uncontrolled Keywords:	Multivariate location-scale mode, spherically and elliptically contoured distributions, invariant differentials, uniform prior, predictive inference, future location vector and residual sum of squares, multivariate Student-t and beta distributions
Fields of Research (2008):	01 Mathematical Sciences > 0104 Statistics > 010499 Statistics not elsewhere classified 01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4905 Statistics > 490599 Statistics not elsewhere classified 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490509 Statistical theory
URI:	http://eprints.usq.edu.au/id/eprint/1049

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