Admissible prediction in superpopulation models with random regression coefficients under matrix loss function

Admissible prediction problems in finite populations with arbitrary rank under matrix loss function are investigated. For the general random effects linear model, we obtained the necessary and sufficient conditions for a linear predictor of the linearly predictable variable to be admissible in the two classes of homogeneous linear predictors and all linear predictors and the class that contains all predictors, respectively. Moreover, we prove that the best linear unbiased predictors (BLUPs) of the population total and the finite population regression coefficient are admissible under different assumptions of superpopulation models respectively.

► We investigate admissible prediction in finite population under matrix loss function.
► An efficient way to study the admissibility of linear predictor is presented.
► We examine two classes of linear predictors and all predictors, respectively.
► The n.s. conditions for a predictor to be admissible are given in the two classes.
► Admissibility of the BLUPs of some population quantities of interest are verified.