All admissible linear predictors in the finite populations with respect to inequality constraints under a balanced loss function

Under a balanced loss function, we investigate the admissible linear predictors of finite population regression coefficient in the inequality constrained superpopulation models with and without the assumption that the underlying distribution is normal. In Model I (non-normal case) with parameter space T1, the relation between admissible homogeneous linear predictors and admissible inhomogeneous linear predictors is characterized. Moreover, for Model I with parameter space T0, necessary and sufficient conditions for an inhomogeneous linear prediction to be admissible in the class of inhomogeneous linear predictors are given. In Model II (normal case) with parameter space T0, necessary conditions for an inhomogeneous linear predictor to be admissible in the class of all predictors are derived.