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

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.