Optimal tolerance regions for some functions of multiple regression model with Student-t errors

Abstract

This paper considers the multiple regression model to determine optimal beta-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. It is assumed that the errors of the regression model follow a multivariate Student-t distribution with unknown shape parameter, nu. The prediction distribution of the FRV, conditional on the observed responses, is a multivariate Student-t distribution but its shape parameter does not depend on the unknown degrees of freedom of the Student-t model. Similarly, the prediction distribution of the FRSS is a beta distribution. The optimal beta- expectation tolerance regions for the FRV and FRSS have been obtained based on the F-distribution and beta distribution respectively.