平衡损失下有限总体回归系数的线性可容许预测（英文）

LINEAR ADMISSIBLE PREDICTION OF FINITE POPULATION REGRESSION COEFFICIENT UNDER A BALANCED LOSS FUNCTION

本文研究了平衡损失函数下正态总体和非正态总体中有限回归系数的可容许预测.利用统计决策理论,获得了非正态总体中齐次线性预测为可容许预测的充分必要条件和在正态总体中齐次线性预测在一切预测类中可容许性的充要条件,推广了二次损失下的若干相关结果.

In this paper, under a balanced loss function we investigate admissible prediction of finite population regression coefficient in superpopulation models with and without the assumption that the underlying distribution is normal, respectively. By using the statistical decision theory, necessary and sufficient conditions for a homogeneous linear predictor to be admissible in the class of homogeneous linear predictors are obtained in the non-normal case, we also obtain a sufficient and necessary condition for a homogeneous linear predictor to be admissible in the class of all predictors in the normal case, which generalize some relative results under quadratic loss to balanced loss function.