TY - JOUR

T1 - Prediction distribution for linear regression model with multivariate Student-t errors

AU - Rahman, Azizur

AU - Khan, Shahjahan

N1 - Imported on 12 Apr 2017 - DigiTool details were: month (773h) = January; Journal title (773t) = Far East Journal of Theoretical Statistics. ISSNs: 0972-0863;

PY - 2008/1

Y1 - 2008/1

N2 - he Bayesian approach under uniform prior is employed in this paper to derive the prediction distribution for multiple regression model with multivariate Student-t error distribution. Conditional on a set of realized responses, a single and a set of future responses have a univariate and multivariate Student-t distributions, respectively, whose degrees of freedom depend on the size of the realized sample and the dimension of the regression parameters? vector but do not depend on the degrees of freedom of the error distribution. Results are identical to those obtained under normal error distribution by a range of statistical approaches such as the structural distribution, structural relations and classical methods. This indicates not only the inference robustness with respect to departures from normal error to multivariate Student-t error distributions, but also indicates that the Bayesian approach with uniform prior is competitive with other statistical methods in the derivation of prediction distribution.

AB - he Bayesian approach under uniform prior is employed in this paper to derive the prediction distribution for multiple regression model with multivariate Student-t error distribution. Conditional on a set of realized responses, a single and a set of future responses have a univariate and multivariate Student-t distributions, respectively, whose degrees of freedom depend on the size of the realized sample and the dimension of the regression parameters? vector but do not depend on the degrees of freedom of the error distribution. Results are identical to those obtained under normal error distribution by a range of statistical approaches such as the structural distribution, structural relations and classical methods. This indicates not only the inference robustness with respect to departures from normal error to multivariate Student-t error distributions, but also indicates that the Bayesian approach with uniform prior is competitive with other statistical methods in the derivation of prediction distribution.

KW - Multiple regression model, multivariate Student-t errors, Bayesian method, uniform prior, prediction distribution, beta, univariate and multivariate Student-t distributions.

M3 - Article

SN - 0972-0863

VL - 24

SP - 35

EP - 48

JO - Far East Journal of Theoretical Statistics

JF - Far East Journal of Theoretical Statistics

IS - 1

ER -