Prediction distribution for linear regression model with multivariate Student-t errors under the Bayesian approach

Azizur Rahman, Shahjahan Khan

Research output: Book chapter/Published conference paperConference paper

Abstract

Prediction distribution is a basis for predictive inferences applied in many real world situations. It is a distribution of the unobserved future response(s) conditional on a set of realized responses from an informative experiment. Various statistical approaches can be used to obtain prediction distributions for different models. This study derives the prediction distribution(s) for multiple linear regression model using the Bayesian method when the error components of both the performed and future models have a multivariate Student-t distribution. The study observes that the prediction distribution(s) of future response(s) has a multivariate Student-t distribution whose degrees of freedom depends on the size of the realized sample and the dimension of the regression parameters’ vector but does not depend on the degrees of freedom of the errors distribution.
Original languageEnglish
Title of host publicationIn: 3rd International Conference on Research and Education in Mathematics (ICREM3), 10-12 Apr 2007, Kuala Lumpur, Malaysia.
EditorsFudziah Ismail, Rohani Tarmizi, Habshah Midi
Place of PublicationKuala Lumpur, Malaysia.
Chapter2
Pages188-193
Number of pages6
Volume1
Edition1
Publication statusPublished - 2007

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    Rahman, A., & Khan, S. (2007). Prediction distribution for linear regression model with multivariate Student-t errors under the Bayesian approach. In F. Ismail, R. Tarmizi, & H. Midi (Eds.), In: 3rd International Conference on Research and Education in Mathematics (ICREM3), 10-12 Apr 2007, Kuala Lumpur, Malaysia. (1 ed., Vol. 1, pp. 188-193). [SE03].