Improved Multivariate Prediction under a General Linear Model

Assuming a general linear model with known covariance matrix, several linear and nonlinear predictors are presented and their properties are discussed. In the context of simultaneous multiple prediction, a total sum of squared errors is suggested as a loss function for comparing predictors. Based on a rundamental relationship hetween prediction and estimation, a very general class of predictors is developed from which predictors with uniformly smaller risk than that of the classical best linear unbiased (i.e., universal kriging) predictor can be constructed.